Have you ever talked over something with your friends? Were there ever differences of opinion? Did to bring up evidence (quotes, etc.) to prove your position? Show how the other person's ideas were weak or faulty? If so, you have participated in a debate. A formal definition of debate by Websters New Collegiate Dictionary 2010 is, "a contention by words or arguments".
Debate is normally done under formal conditions. Most high schools and colleges have debate teams that travel around to other colleges and high schools to debate on pre-specified, "resolutions".
There are two major forms of debate known as the Lincoln Douglas style, and the Team Policy style. The Lincoln Douglas debate has only one competitor per side, each person is on their own. The resolution usually deals with values (pragmatism over idealism; which is best?). Each person prepares for both sides of the case because they do not choose which they will do. Team Policy debate deals with policy issues, teams of two work together to support their view and break down the opponent's. Again, each team prepares for both sides of the case.