Something that is hush-hush is secret and not to be discussed with other people.

For example:

The hush-hush affair between the two celebrities created a buzz.

In the end, he was forced to resign, but it was all very hush-hush.

They were desperate to keep the marriage hush-hush. 

Apparently, there’s a very hush-hush project underway up north. 

Tradução: em segredo, sigiloso, escondido.