Original: In Canada, "the 51st state" is an emotional trigger phrase generally used in such a way as to imply that if a certain political course is taken, Canada's destiny will be to become "the 51st state".
Simplified: 51st state, is a humorous term in American politics that refers to (talks about) a land, which is not a part of USA, but is thought to be added to the United States, becoming the 51st state. Sometimes "51st state" is said seriously (about American Samoa or other territories).