cough cough is used to subtly imply that you know something that someone else doesn't. The person who it is "used on" will then begin to suspect something is suspicious with the phrase "cough cough" and will begin to wonder what it means. Mostly, "cough cough" is pronounced as a word, instead of being actually "coughed out".

when you're hungover as shit after a spending a night drunk as a skunk

when your not in agreement with something but the other person things you’re in agreement

The act of semi-discretely littering in a way that looks as though accidentally dropping the trash while suddenly and deeply coughing.

1. any act involving sexual activity with another of your species