From Wikipedia (http://en.wikipedia.org/wiki/Mixed_martial_arts):
Mixed martial arts (MMA) is a full-contact combat sport that allows the use of both striking and grappling techniques, both standing and on the ground, from a variety of other combat sports and martial arts.
MMA can be broken down in three different components: stand-up, taking down your opponent and the ground game. In the past, fighters came from one MA or background. Modern MMA however has evolved to its own style, with fighters blending many different MA's into their game.
Fighters fight in a cage with minimal equipment on. During the matches, mixed martial arts fighters only wear thin gloves and are barefoot. Fighters are allowed to punch, kick, grab or do anything else to their opponents to win the matches. This stays true to the sports Brazilian fighting roots of Vale Tudo, which translates into English as “anything goes.”
The few rules that the sport does have are similar to boxing and wrestling. Fighters can win a mixed martial arts match by three different ways. A fighter can knockout or hold into submission his opponent, or win by a judge’s decision.