Put simply, a referral bonus is cash (usually in the form of bonus bets) that you can earn from a betting site by getting a friend, family member, acquaintance, random person on the street, or your boss to sign up to your betting site.
Typically your betting account will have a unique referral number or code that you can give out to a certain number of people to use when they first sign up, deposit, and place a bet that can often net you both some bonus bets.
Example: Caesars Sportsbook allows players to refer a friend and get $100 in bonus bets once they deposit and bet!