Fiasko is right - "someone has or someone's got nothing on you" means that somebody is comparing you to someone else and you are smarter, harder-working, more polite, more beautiful, etc. The expression compares your qualities, knowledge or skills to someone else's qualities, knowledge or skills.
But there is also another meaning for the expression. It is used when the police investigate a situation and they think they know who did a bad thing but they have no evidence, no proof, no way to prove that the person is the one who is responsible for the problem. So in a sentence: The police are sure you did it, but the police have nothing on you (nothing to prove it was you who did the bad thing).