A fib is a lie.
Fibs are usually small lies that someone tells to impress their friends or colleagues. Fibs involve elaborate stories and people who tell fibs are usually addicted to them.
You also have the noun "white lie" which is a harmless or small lie you tell to avoid hurting somone.
A: You know, yesterday I met a beautiful girl. I invited her to a drink and she gave me her phone number.
B: That's a fib! Yesterday I talked to your brother and you were grounded at home!
Come on, tell us a fib in a comment! We'll believe you! ;-)