He is the brother of Susan Carter and uncle to Kate and Danny Carter.
Background
Ted appears to be the cool uncle type, and joins in with the joke when Kate complains about ruining her life. He was helping the Carters move into their new place when they run into Sam and Dean. When they say they can't move into the house, Ted gets angry, but leaves with the family to the motel. He later returns realizing the lies Sam and Dean told due to his experience as a construction worker. Later on, he finds writing on the walls and assumes it was Danny.
Then strange things happen and Sam and Dean tells them its ghosts, which Ted finds hard to believe. When its proven its not a ghost, Ted is happy to be proven right. Then Danny goes missing and Ted and Dean go to look for him. They find space in between the walls, and look around in them. When Dean goes down the hole and leaves Ted alone, the girl comes up behind Ted and stabs him repeatly. Dean carries Ted's body out.