He first got his big break when he became Zim's opponent in the Skool Election after the last Student President had a mental breakdown (characterized by the Skool as a "loss of Skool spirit"), and was supported by Dib. With limited intelligence, he relied on Dib's help to win the election, until his mindless confidence and idiocy took over.
Nevertheless, he won, and was subsequently brainwashed to act intelligent, speak with a British accent, and praise the Skool constantly.
He reappears as a cameo in Issue 16 of the comic series, when Zim has him dressed up as Santa Claus as part of Zim's campaign to try and scare Dib. Notably, his one line of dialogue indicates a return to his normal low level of intellect. Presumably, this either means his time as Student President ended and he was returned to normal, or else it's merely a continuity error. He has also reappeared in a cameo in Invader Zim: Enter the Florpus, holding hands in the peace circle.
Willy is a large, bald male who wears a light-green, undersized shirt with a cat on it, and usually has his tongue sticking out of his mouth (causing him to slur his speech often). Willy is dirty and, seemingly, has a bite taken out of his ear.
There is also a kid in the original pilot who strongly resembles him.