When you feel compunction you feel very, very sorry, usually for something you did to hurt someone or mess something up. When you feel no compunction, you're not at all sorry.
The noun compunction comes from the Latin verb compungere, meaning “prick sharply.” When you feel compunction, you feel a sharp prick of your conscience. The word compunction is often used in the negative in phrases like “without compunction” or "no compunction." You might say that the burglar acted without compunction when he stole your baseball card collection.