Ragtime is a style of music that was developed in America in the late 19th and early 20th Centuries. Its bouncy, cheerful sound was most popular in lower-class bars and clubs; but the style proved to be amazingly versatile, capable of great sophistication and emotional lyricism, while still being fun.
The style of music experienced a huge resurgence in popularity during the 1970s, when the award-winning movie The Sting resurrected the little-known Scott Joplin rag tune 'The Entertainer' and it was turned into an instant hit.
Ragtime is characterized by a syncopated melody and a duple bass, though some typical rag tunes contain sections that do not fit this mould. For example, Scott Joplin's 'Pineapple Rag' has four themes, only two and a half of which use the duple bass. 'Pineapple' uses an A-B-A-C-D format. Themes A and B are classic ragtime. Theme C, however, contrasts the bounciness of the first two themes with a flowing, lyrical melody. Finally, theme D re-emerges from the emotional depths of theme C by mixing the moods of the other themes, employing the characteristic ragtime bass figure only half the time.
The hardest aspect of playing ragtime piano is dealing with the fact that you're playing three parts (a bass line, a harmony, and a melody), most likely without the benefit of having three hands. This means that the left hand must perform double-duty, playing the bass part on the first and third beats of each measure and the harmony on the second and fourth. The best way to accomplish this is to use the smallest finger exclusively for the bass part, and to use only the remaining four fingers for the harmony chords. Breaking this rule will lead to your fingers tying themselves into permanent knots, which can be damaging to your career as a pianist, not to mention embarrassing in social situations.
The second trick to playing ragtime piano is the use of the sustain pedal to smooth out the sound. Your left hand is literally bouncing between two parts (but it can't be in two places at once), and the music would sound very choppy if it weren't for the sustain pedal, which tells the piano to pretend that you have not let up on any of the keys, even if you have. The best technique is to depress the sustain pedal on the odd-numbered beats (when the little finger is hitting the bass note) and release it after the even-numbered beats (when the other four fingers are playing the chord.) This effectively sustains the bass note for two beats, producing the so-called 'two-beat' feel that was popular in all sorts of ragtime-era music.
Finally, for maximum authenticity, ragtime should be played on an upright piano that is ever so slightly out of tune. Luckily, there is no shortage of pianos with this specification in the world.