Wikipedia explains it much better than I do:
http://en.wikipedia.org/wiki/Multiplayer_online_battle_arena
Basically two teams each trying to take the base of the other, but first they have to level up by killing
NPCs while avoiding being killed by the other team.
It's a really fun game style that has spawned a number of popular games: DOTA, DOTA2, League of Legends, SMITE, and many more.