Hurries is a statistic kept for defensive players, usually defensive linemen, when they "hurry" the quarterback into throwing the ball before he is ready. Hurries often result in incomplete passes or even interceptions.
A quarterback hurry is counted when a defender either forces a quarterback out of the pocket or pressures the throw. It doesn't necessarily mean that the defender actually forced the quarterback to make a bad throw. Hurries are often a good indicator of a team's pass rush. Just because a player is not getting sacks, it does not mean he is not a good pass rusher, because hurrying the quarterback into a poor decision can be just as effective.