Terrence is the father in a cool family.
Homer tracked him down when looking for the Devil Donuts vendor. He was shocked to find out that Terrence was a father as he seemed too cool to be one. Homer and Terrence quickly became friends. Terrence and his family moved into 740 Evergreen Terrace, next door to the Simpsons, and they added a gate between their gardens to allow easy access to each house.
At T-Rex's birthday party, Bart had a fight with T-Rex and Terrence blamed Homer for bad parenting, effectively ending their friendship. The two families started to feud until Ned stepped in and tried to make them friends again. Eventually, a lot of other cool people moved into Springfield, due to a review of Springfield that Terrence had written. A fire broke out on the Devil Donuts van and there was no water to get to it to put it out. Terrence was then pleased when Marge put out the fire with the formula baby milk.
After finding out that it was no longer cool to be in Springfield as all the other cool people had moved in, Terrence and his family left Springfield for good.
Terrence seems cool to most average people. He follows a set of standards which he considers trendy and doesn't accept anyone who doesn't agree with these standards, as seen when he broke his friendship with the Simpsons. He refuses to stay anywhere where it is considered not cool or trendy as there are too many cool and trendy people there.