Used to describe anybody famous who is not in your face about it all.
Originates from a major rock star who goes against the stereotype and isn't interested in making his off-stage and away-from-music life public. When being interviewed, he is likely to say that there's nothing about himself that's really remarkable, that he's just a guy. And when a cop saw him walking about at night and asked him for identification, he's cool about it all and made no fuss, unlike some small town politicians may do.
Therefore, a Big Zimarooni is a real nice guy.
Did you see the Dylan interview on 60 minutes? Wow, he is The Big Zimarooni!