A woman is speaking on the phone about taking precipitate action. Her husband overhears part of the conversation, and thinks she is talking about rain (precipitation).
--It's going to be sunny, he says.
What we have been speaking of has nothing to do with the weather, she replies.
"To have nothing to do with X" means to be entirely unrelated to X.
A child overhears her parents speaking in hushed tones. She thinks they're going to be sending her to bed early.
-- It's nothing to do with you, says mother. We're talking about your brother.
Same meaning as "it has nothing to do with you."
EDIT: My treating "It's" in It's nothing to do with you as a contraction for "it is" has been challenged by Drew. I think in that locution the contraction stands for "it is", not "it has"; there is a variant that goes:
-- It's got nothing to do with you
where the contraction does mean "it has".