What is MOBA? I know MOAB is the mother of all bombs, but...
"Multiplayer Online Battle Arena"
Did you ever play Dota?
All players take a hero character. There are 2 Teams each with a base. AI controlled mobs will come in waves from each base and try to get to the opposition's base, fighting stuff along the way (other AI or player heros). The mobs travel down paths called "Lanes". There are normally multiple lanes and the Heros can usually take shortcuts to switch lanes.
The players try to escort their AI mobs to the other base and destroy it. They do this by "Pushing" lanes, destroying the opposition AI there (which are much weaker than the heros but greater in number).
Opposition heros are normally doing the same. You earn gold (or credits or whatever) by doing stuff (killing opposing heros is often a good source.. getting farmed, or killed a lot, is often bad) and it can be spent on items in a store to beef up your hero.
Heros normally level up and are normally split into different categories such as strength heros (good melee characters) and agility heros (good range or utility characters) or int heros (good magic) and usually have special abilities unique to the hero.
Of course various Moba games have different twists on the genre.
Apparently a good place to start (and a free to play) is LoL: League of Legends. Never really been into the genre myself though so I'm sure some others will have some better descriptions / starting point suggestions.
