The Triad is a Chinese crime syndicate which allied with Demona after she turned to stone on their yacht belonging to one of their leading members, Gong Li. They had, in their possession, a gargoyle egg, for several centuries. After taking command of the Triad, Demona attempted to use a bolt of lightning to hatch the egg on top of the Empire State Building. Yes, it is as asinine as it sounds. One can only assume that this wasn't actually a gargoyle egg and Demona was lying to Goliath
Their scheme was foiled by the Manhattan Clan, most of the members of the Triad arrested, and Gong Li fled with the egg.
Real World Background
The Triad is a real Chinese crime syndicate, with many branches all over the world. It is unknown if they worship Demona as a god, but it'd be both much cooler and much lamer if they did.