"Give me a hand, could you?" This sounds like Yoda speak in my opinion. I would say "Could you give me a hand?" instead. This phrase is more polite and resembles a request. "Give me a hand, will you?" is more of a command. When you say "will you" at the end, it's more of an insistence because it kind of has a slight bearing that the person you're talking to isn't helping you. "Will you give me a hand?" is about the same as "Could you give me a hand?", but might seem a tiny bit more commanding since "could you..." is a little polite. Though, I wouldn't really notice the difference either way.

It is a short way of expressing "Will you do this?" or "Will you help me?"