Yes Taima is right! Imagine a bag and you don't know what's inside, and suddenly - a cat appears! You have told somebody some information - perhaps a secret - and now the truth is out - 'the cat has been let out of the bag' - the cat's out of the bag! :)

This idiomic phrase used when a secret revealed by someone. We can also say: "Let cat out of the bag"( means to reveal a secret).