it means don't let someone know the surprise
This classic saying means to tell a secret or something that shouldn't have been said. If someone lets the cat out of the bag they spoiled a surprise or told a secret. Here's how to use it in a sentence: "Jeremy let the cat out of the bag on Friday so Bob knew we were throwing a party that night." So, Jeremy told Bob about the party, 'let the cat out of the bag', and told the secret early.
"Don't let the cat our of the bag" mean "Don't tell my secret."
"Letting the cat out of the bag" is telling a secret, usually inadvertently.