A colossus (plural colossi) is a type of mountain giant. Their flesh is stony and giant crystals stud their shoulders, back, and skull. If they are killed, they can be mined after they have been looted. They can be found in Outland and Azeroth.
In Hellfire Peninsula, after a red crystal fell to the surface from the sky, colossi were summoned and led by King Goliathon. The red crystal that summons them and drives them mad was created by Pathaleon the Calculator for his master, Kael'thas.
There are also colossi found in other places in Outland. Some of these colossi can be found in Netherstorm and other locations of the shattered world. These colossi, at least the ones in Shadowmoon Valley, are led by Behemothon, King of the Colossi. The Illidari are negotiating an alliance with them, abortively. Behemothon is likely Goliathon's successor after he was killed in an earlier quest chain.
Colossi on Azeroth are found in Northrend, one is in the Nexus and others are found in the Halls of Stone. The ones in the Halls of Stone were made when the iron dwarves turned their weapons on Ulduar, tunneling through its walls and carving out monstrous crystal giants from the very heart of the mountains surrounding the city. Many friendly colossi can be found helping the earthen, and players, of Bouldercrag's Refuge.
This section concerns content exclusive to Cataclysm.
As colossi are implied to have some sort of connection to the titans in Wrath of the Lich King, this could imply that the colossi of Outland may be further evidence of previous titan involvement on that shattered world (along with ancients and other animals shared by Azeroth and Draenor).
They also appear to be a type of earth elemental under certain conditions. It is unknown if this applies to all colossi, or if it is just some entities reusing the model.