Taken from Wikipedia -
The genre takes its name from Defense of the Ancients (DotA), a popular Warcraft III mod, and games in this genre are often referred to as "DotA-style", "Dota-esque" or "DotA-based" games, as well as "DotA clones", or sometimes simply as "DOTAs". The term "AoS-style game" or simply "AoS" is also commonly used, referring to the Starcraft custom map called Aeon of Strife, which influenced DotA. Riot Games coined its own term, "Multiplayer Online Battle Arena" (MOBA), while Valve refers to these games as "Action Real-Time Strategy".
Welcome to the mainstream!!