This poorly constructed episode of House featured the main character sitting outside the principal's office because he lied about his identity and got into a fight while giving a speech at Career Day.
He was at this school because he wanted to get Rachel into it. He thought that might be a way to prove to Cuddy that he actually does care about her and her happiness.
Through a couple flashbacks, we saw just how angry Cuddy got at the small things - such as House using her toothbrush - all of which led to her accusing him of being nothing but self-centered. House pretty much admitted this in the end, inspired by a couple students he met at the school, but also said he could do better. He wanted another chance with Cuddy to work on his selfishness. She gave him to him.