Útgard-Loki is the King of the giants in a place called Útgard. When Thor, Loki and Thialfi visit him, the King invites them to participate in a series of epic contests to prove their worth.
This giant is a powerful sorcerer as he has created illusions that can fool even Loki, who is a masterful illusionist himself. The entire fortress of Útgard and its inhabitants, but also the friendly giant Skrymir, were created by him to fool to intimidate the Aesir.
Útgard-Loki is no family of Loki (that we know of).