This term refers to the number of times a quarterback throws the receiver the ball. It is usually referenced when talking about the receiver. A quarterback's total targets will not always equal the number of attempts, because some throws result in interceptions, and some throws are intentionally off target.
The number of targets a particular receiver totals indicates how useful he is to the team. A quarterback will obviously want to target the best receiver, but this can easily backfire. A receiver with a lot of targets is a dead giveaway for defenses to cover. Quarterbacks must spread out their targets in order to keep the opposition guessing. A quarterback will typically throw the ball to a receiver no more than 10-12 times per game. There are exceptions, of course, but any more than that and the offense runs the risk of becoming lopsided by always favoring one receiver.