Truman wanted to leave the show because he discovered that everything in his life was artificial. He was living inside a enormous soap opera that went on for twenty-four hours a day, 365 days a year, and had been running ever since he was a newborn baby. Even the woman he was supposedly married to was only a paid actress who was always promoting products by pretending to be showing and explaining them to Truman. His best friend was only another actor paid to pretend to be his best friend. He realized that he was actually a prisoner on this island which was nothing but a big stage set. (The story was reminiscent of some of the old low-budget shows on The Twilight Zone on black and white television.)
Truman's main motivation was to find a girl he had once met who warned him that he was a virtual prisoner and that his whole life was nothing but a scripted television program being watched all over the world via hidden cameras and microphones and being used to promote all kinds of products and services. This girl was abducted and spirited off the island while she was in the process of telling Truman the truth about the whole enormous production. I believe it was explained to him that she was an escaped lunatic, but he always remembered her and hoped to find her again someday. When the movie ends, he is evidently going off to join that girl in the world of reality.