Other forms: discreetest; discreeter
Discreet describes someone or something that is appropriately quiet, prudent, and restrained. If you are wearing a discreet gray suit, it is unlikely that anyone at that business meeting will notice you.
Often people use discreet not only to indicate modesty or carefulness, but also to show a sort of secretiveness along the lines of “You're going to keep this a secret, right?” If no one in your family knows that you like to dress up as a bear, but then your cousin finds out, you may ask him to please be discreet.