A fib is a small lie. If you think your friend's haircut looks strange, but you tell her you love it, it's a fib.
When you tell a fib, you fib. The thing that distinguishes a fib from a lie is that a fib isn't terribly important — it's minor or petty. You might fib to protect someone's feelings or to save yourself a long explanation about exactly why you're late to work. The origin of the word fib is uncertain, but it may come from fibble-fable, or "nonsense," which in turn comes from fable.