In League of Legends, ADC is the Chinese prodigy. This is a position in the game. This is a game that was developed for Microsoft Windows and it was published by Riot Games. You can get the details on http://en.wikipedia.org/wiki/League_of_Legends.
ADC, "Attack Damage Carry", is the term people use when they are going to go in the bottom lane and they will do the most attack damage of the game. This means that they will exclusively buy items to increase their damage, critical chance, life steal, or attack speed.