A fortnight is fourteen nights — two weeks. This is a fancy, old-fashioned term you don't hear much anymore.
Fortnight is not a word we use very much in this country, unless you want to sound very British, very 19th century, or both. If you read old British novels, you'll read about a lot of fortnights, and the word is still in use in Great Britain and some former British colonies. It comes from the Old English, literally a shortened form of fourteen nights. People sometimes use it when they're discussing their vacations or their pay schedules. Here, we just say two weeks.