There is no difference. 'Favor' is the American spelling, 'favour' is the British spelling. It's the same word with the same meaning.

Like Paul said, there are several differences between British and American spelling. This, an example of -our words, is one of the most common (favor/favour, color/colour), along with -ise words (like apologise/apologize). This is a good source: http://www.oxforddictionaries.com/us/words/british-and-american-spelling

Nothing