I often read the terms "first degree murder", "second degree murder" and "third degree murder" in US newspapers. I'm not from the USA, and these terms are quite confusing to me. I've tried reading the Wikipedia article on it, and while it does give a small amount of explanation, it essentially is 2 double-stub length paragraphs based around various jurisdictions, with a bunch of links to specific types of murder and methods of murder.
What's the difference between first degree, second degree and third degree murder?