To answer this, we must first consider where wizards came from. Yes, their roots lie in mythology, but if you were a wizard being asked that, you might have looked through this question's surface and into its meaning.

Wizards were a part of ancient fantasy, and have survived all the way into contemporary fantasy, for the same reason as elves, ogres, or knights. They are all extreme examples of the sorts of creatures that exist in reality, and so they are archetypes and can never die. Who among you hasn't confronted an ogre or 15 in your lifetime? When a soldier trains daily for battles he prays will never come, is he not acting as a knight? When an old relative, who has always acted appallingly childish up until this point, comes through for you in trying times with a powerful bit of wisdom, has she not been playing the role of the elf? Learn what's in a wizard, that way when you meet one you'll know what you're dealing with, and more importantly, so the next time you hear someone say wizards aren't real (or witches or whatever) in that haughty matter-of-fact tone mastered by so many, it won't be their sensibility you recognise but yours, at realising how foolish they sound.

Talent

This is at the heart of what defines a wizard. A wizard, by his very nature, will be decidedly adept in any given intellectual field, whether it be linguistic, logical, spatial, musical, kinesthetic, interpersonal, intrapersonal, or any combination thereof. This is not to say a wizard must be the best there is at each of these things, but simply that it will all come more easily to him. There may also be exceptions, such as a wizard born without the ability to understand or appreciate music at all. These exceptions usually happen to a wizard through the natural balance that tends to make itself part of their life, whether welcomed or not, and is discussed further on. Regardless, the innate talents of a wizard set them apart from their competing peers, putting them to shame and making the wizard easily identifiable. It is on this concept of talent that the usage of the word wizard has thrived. Although lately, it may be better known in the more mangled form of wiz or whizz, (as in 'Paul may be a maths whizz, but I like him anyway.') but most people have taken the time to become familiar with the entire word instead of just the good half.

Observation

The short story Debt of Bones by Terry Goodkind offers a scene that truly personifies the way in which this quality can set a wizard apart. In it, the character Abby, upon meeting the First Wizard Zorander for the first time, is astonished to see several people speaking with the First Wizard simultaneously. A tad unnerved and quite sceptical about this situation she finds far more difficulty in carrying on her part of the conversation with the First Wizard than he does with his, in addition to the many other conversations in which he is already actively participating. Zeddicus Zorander has no difficulty listening comprehensively to what, for any other person, would be utter commotion. Later on in the same story, Zedd is able to hear Abby again under equally impossible circumstances, when her frantic message is called to him from much too far away.

With most people, not listening to others is an indispensable part of their daily lives. However, a wizard, perhaps because of some error in his brain, is characteristically helpless to conform to society. As such, they will be the person who is always listening. A similar aptitude to read between the lines of a conversation will also make itself obvious, as well as an acute knack for seeing things that don't belong or are at least out of the ordinary. They will sometimes also display a keen sense of surroundings, except those bookish types that are always spaced out. Many wizards even sleep with their eyes open, just to push the point.

Limitless Comprehension

Again, in order for Zedd to accomplish such feats as multiple conversations at the same time, he must have kept up with everything he was hearing. Comprehension is a big part of listening (in some circles). A wizard should have no problem absorbing information that would make a normal person fling their hands up in the air in disgust. Don't confuse comprehension with talent. It is one thing to learn something quickly. The point here is about the limits of a wizard's mental capacities - as in there aren't any.

Selective Memory

Because of the unique quality wizards possess of being able to absorb substantial amounts of information, there must be balance elsewhere. Unfortunately for their friends, this balance may come in the form of forgetting their names, or many other things most people would be insulted to have forgotten about them. This forgetfulness also extends to pretty much anything else save what has been embedded into their memory through bizarre and uncontrollable criteria that can only be described as personal. There's only so much room in anyone's memory, and when someone can't recall their own anniversary because they instead unconsciously chose to remember the exciting new discovery at work someone made, that person is displaying decidedly wizard-like characteristics.

Intrinsic Motivation

All right, but in order for their work to claim those coveted priority spots in the wizard's memory there must be some kind of self-actualisation going on there. A wizard can't just take any job just because it's the family business, or even because he happened to be raised by the local clockmakers' guild. Furthermore, it would be a rare sight indeed to see a wizard working in the military or as a policeman. It would simply go against their overwhelming instinct for independence. This is because wizards, as a people, are driven not by society, power, or even benevolence, but by an internal desire to fulfil themselves as wizards. Many wizards are born to be servants of the people; they will use their talents in protecting the masses. Conversely, there are some that must live unmindful of fellow humans. In the Earthsea Cycle by Ursula K Le Guin, Ogion is perhaps the most powerful mage of all, yet he can only live contentedly and fulfil his purpose in life as a hermit. While still more wizards will exist perhaps only to invent, with absolutely no concern for other people or even in what way their inventions will be used. Regardless of where this motivation leads, the significance is its effect. Wizards must always live in freedom in order to realise themselves, but ironically they are inevitably victims of their own nature. While truly you might think that for all their power they would have more freedom than any, in the end, a wizard's life is not his own. Instead, it is the product of their intrinsic motivations, which will send them off to live as a wizard, willingly or kicking and screaming every step.

Behavioural Eccentricities

Being honest, all these wizardly attributes leave little room for social niceties. Some wizards are just plain weird, and often an internal battle between insanity and genius must be waged and won before the outward conflict can even stick its head out to see if it's show time yet. The true wizard will always triumph under said pressure, while the inferior models usually just burst into madness at some intervening point. There are too many examples to name them all, but rest assured all the cool wizards are doing it these days. Harry Potter usually gets the whole school to think he's crazy about once a year. Don't panic, this doesn't mean that the kid in science class that wore his socks inside-out for good luck was a wizard, he could easily have just been an idiot.

Wisdom

Firstly, what exactly is wisdom? Is it judgment? Possibly, but when's the last time you heard about a Norse god giving up one of their eyes to be allowed to drink from the Well of Sound Judgment Skills? Wisdom is so much more, it is a kind of active insight into the nature of truth itself and wizards have got it in spades. When a party of adventurers runs into a difficult decision, even the leader will look to the wizard, and their real world counter parts are no different. If you're grappling with an extremely tough problem and your party does not have a wizard, please don't shake a quiet kid and demand to know if he's a wizard.

Creativity

There is an informal understanding that the best wizards are the most childlike. Why? It's simple, a wizard's power and imagination come from the same place. The ability to shape magic into spells is not accidentally the same sort of act as the shaping of clay into pots or mental images into paintings. Wizards are artists, and so it follows that their spells must be works of art. Originality and imagination abound in the mind of a powerful wizard. They simply cannot conform, and this goes for their ideas as well.

Harmony

The harmony wizards must have in their lives to operate properly is, as usual, just an amplified metaphor for the balance ordinary people find they require in their lives as well. For instance, just as a normal person will become exhausted after a two hour-long argument with their spouse over who's the best driver, a wizard may go into a year-long coma after trying to break the mind of Yorg, the Mindsplitter Demon of Caerthos. All right, that's not really the kind of balance being discussed here; it's just a good lesson for people in general.

A more appropriate example might be how just as an ordinary person would probably do best not to pretend they're somebody they're not for fear of forgetting who they really are, a wizard probably shouldn't frolic in the body of a squirrel too long for fear of forgetting they're a human and getting stuck as a squirrel forever. Many times a wizard will be unable to cast a powerful spell, not because they are not up to it, but because the consequences of it will destroy them. The essence of it is that balance is a wizard's worst enemy. Case in point, Richard Rahl, despite his best efforts not to be a war wizard, finds himself killing people an awful lot. So as a balance, eating meat now makes him sick. When he doesn't have to kill, he can then eat meat again. By the eight book, Naked Empire, (Warning, Plot Spoiler!) Richard has become so powerful that he no longer has to kill simply to survive, but he begins to experience headaches that are killing him. This is when Richard learns the meaning of the wizard's eighth rule: deserve victory. He realises that if the killing he does really is the right thing to do then he wouldn't need to balance it out with anything else, and by simply eating meat again, as he should, harmony is restored and his fatal headaches cease.

Foresight

Many wizards display an unusual knack for seeing what's coming. Sometimes this is in an instinctive sense, like when one may prudently ditch his friend in an abrupt flash of clarity, just before a clumsy and drunken telepathic offensive against Yorg, the Mindsplitter. Many times this foresight is displayed in a concrete manner, such as sensing something important before it's about to happen, like the 'spider sense' of Spider Man, the superhero. On other occasions it can come in a more abstract way, like sensing something important before it's about to happen - like Spiderman the movie. (Who thought that was going to be any good?!)

Cunning

Wizards are devious. They'll trick anyone if it means achieving their goals, even the good ones. Wizards are often feared, not because they are rumoured to make you sterile if you touch them, but because of their conceivably inhuman talents for the subtle and deceptive. When Merlin got it into his head that Camelot should have a king of his choosing, he simply used magic to fool Arthur's mother into thinking Uther Pendragon was her husband so that they would conceive Arthur. Probably not the circumstances most people would choose to be born under. Merlin then planned out the whole Sword in the Stone contest. He may have even created the Round Table. So basically the entire kingdom of Camelot was just his brain child. This kind of thing explains the confusing behaviour of most villagers to cower away from wizardly folk and spread rumours about them behind their backs.

Influence

A wizard's natural sway over the minds of others is as infamous as his cunning intellect. When they put their minds to it, they can get just about anyone to do just about anything. Many wizards find that they must use a few people in order to protect the rest. This is a great burden, but they seem to do it anyway. Using other people as tools may sound wrong, but it's for the greater good, and usually it's the only way to do business. Imagine what the Lord of the Rings would have been like if Gandalf had tried to take the One Ring to Mount Doom himself. Or what if Yoda had tried to kill the Emperor instead of Luke? If being a wizard means you have more brilliance, daring, and inner strength compared to the ordinary folk, then it really becomes your responsibility to get them to do what you want. The same line of thinking is used in politics, except in reverse, so that it is the people with the least brilliance, daring, and inner strength who lead. This illustrates an example of why many people find fantasy too silly to read.

Further Reading

• Wizard Lore - An Introduction
• Wizard Lore - Lingustics of Note
• Wizard Lore - Natural Predators
• Wizard Lore - Spell Categories
• Wizard Lore - Loose Ends
• Wizard Lore - Concluding Q&A