A pyramid scheme is in many ways like a chain letter. Someone will ask you to join the scheme by sending them a small amount of money (usually £1 or $1). Once you have paid them you advertise the scheme yourself and everyone who you get to join sends you money. People usually advertise the scheme by email or in newsgroups and claim falsely to have made thousands of pounds. If you get one person to join you break even, if you get more people to join you make a profit.
At first glance it may seem simple; everyone gets a handful of people to join and makes a nice profit. However, all that money can't appear from nowhere.
Why Doesn't it Work?
The amount of money in the scheme is, in total, zero. Some people have positive amounts of money and some negative (ie they've paid but not got anyone to join, therefore they have lost money). The longer the scheme has been going the bigger it gets. In theory, as people get more than one other person to join it grows exponentially. Everyone has profits except the bottom rung that have paid but not signed up more people yet. So there are many more people who have lost money than gained.
Of course you can make money - but that depends on getting other people to join and for them to give you money. This is very hard as most people will see through the scam. So, to make money you must expend a lot of time and effort to get people to give you money. A few people, then, will work really hard and make some money (no doubt not nearly as much as they claim) and the rest will waste their money and not get any return.
The only person who is odds on to benefit is the person who started it all because they haven't paid anyone to join. Because the starter is making a profit there is a negative amount of money in total between the other people in the scheme. So more money is lost than won by people who pay to join these schemes.
Like most types of gambling the risks outweigh the potential rewards. It's not worth wasting your time and money on pyramid schemes.