To refund is to give money back, especially when someone isn't satisfied with an item they bought or the service they got. If you complain that your restaurant food is undercooked, the manager may refund your money.
When you don't actually get what you paid for, you deserve a refund, or a repayment of the money you spent. Most businesses will refund money to unhappy customers, and when you return something — like a pair of pants that doesn't fit — you'll also get a refund. The verb came before the noun, and it originally meant "to pour back," from the Latin root fundere, "to pour."