MMA means mixed martial arts.
In MMA you can use punches,kicks,grappling,submission moves.
Usually fighters use Brazilian Jiu-Jitsu and Muay thai.
Roots of MMA comes from Ancient Greek. In Greek there was sport called Pankration which is similar to modern MMA and it combines boxing and wrestling. Another example is Leitai from Ancient China, which is like pankration mix of boxing and wrestling. It was long road for MMA to become the thing we now know and love.