Basically "mixed martial arts" means a set of martial arts skills drawn for many different styles (kung fu, judo, karate, etc.) that are not used as formally as one single style is. Think of it as a fighting toolkit, pick what you know how to use and that will help the fight you're in.
A mixed martial artist is someone who studied more than one form of Martial Arts! i.e. Boxing, Wrestling,Judo, Jiu-Jitsu, Muay Thai etc. etc. I personally am training in boxing and actually goin to start Judo tonight!