Why are NP problems called that way (and NP-hard and NP-complete)?

Really.. I'm having the last test for graduation this Tuesday, and that's one of the things I just never could understand. I realize that a solution for NP problem can be verfied in polynomial time. But what does determinism has to do with that?
And if you could explain me where NP-complete and NP-hard got their names, that would be great (I'm pretty sure I get the meaning of them, I just don't see what their names have to do with what they are).
Sorry if that's trivial, I just can't seem to get it (-:
Thanks all!