Like we said: most played game in the world. Riot Games pushed it heavily as a professional e-sport, and it has long since eclipsed the original DotA's popularity. However, LoL has many distinct differences from DotA, most of which simplify the game to some extent. LoL currently competes with several other games that originate from DotA, including its own direct sequel, Dota 2.
League of Legends, like all MOBA games, stems from Defense of the Ancients, originally a Warcraft 3 custom map, which itself was based on Aeon of Strife, a Starcraft custom map.