Smiling all in a person's face, trying to gain their favor. Usually a person that is skinning and grinning is being fake or phony, flattering, or flirting. Trying to impress or befriend a person. Often they don't really like or respect the person and since they aren't being sincere, they are just skinning and grinning.
person 1: My boss always gives me so much more work to do than everybody else.
person 2: Really? Why do you think that is?
person 1: I don't know, probably because I'm not always skinning and grinning in his face like the other people there.