A fawn is a young deer, but it's also a verb meaning to try and win favor by flattering. You might fawn over Bambi if you want to hang out with the cute and fuzzy gang.
As a verb, fawn either refers to an attempt to get on someone’s good side, or, oddly enough, to give birth to a deer. If you're a human, fawning is an age-old art that might get you what you want but can be very unattractive. If you ever come into possession of a great fortune, watch out for sudden friends who want to fawn over you and shower you with presents. They probably have dollar signs in their eyes.