A cough is a reflex in which your throat or lungs are cleared by a sudden, sharp burst of air escaping. A bad cough can make it very hard to sleep at night.
A cough is evidence that someone's sick, and it's a verb as well: "She began to cough and couldn't stop until someone brought her a bottle of water." You can also describe a cough-like sound that an engine makes when it's not working properly as a cough. The Old English source of cough is coughen, from a Germanic root — every version of the word is imitative, the word itself sounding like a cough.