Mum’s the word is an expression used when you tell someone or agree with someone to keep a secret.

For example:

I don’t want anyone to know that I’m pregnant yet, so mum’s the word.

Mum’s the word on tonight’s surprise party.

I heard Elaine’s parents are out of town tonight, so I’m gonna go over. Mum’s the word!

He also said not to mention that I was paid to write an update for him, so mum’s the word.

Your secret is safe with me. Mum’s the word.

Tradução: ficar de bico clado, nem um pio, é segredo.