An Exacta wager is putting together the top two finishers of a race in the exact order. It is tougher than traditional Win, Place, and Show wagering, but obviously not as difficult as attempting to hit a Trifecta or Superfecta.
There are many ways to place exacta wagers, probably the most common a two horse Exacta Box.
A $2 Exacta Box with the 1 and 2 horse would cost a horseplayer $4. If the race comes in either 1-2 or 2-1, the horseplayer wins. Any other combination, and the ticket is worthless.