A more "technical" reply might be: "the range for which the maximum ordinate of the projectile does not rise above the danger space (or beaten zone, or vital zone of the target)."
In other words, as a bullet leaves the muzzle, it rises relative to the line of sight, because the barrel of the rifle is pointed slightly upwards and the sights or scope are higher than the muzzle. At some point, the bullet crosses the line of sight and continues to rise as it goes downrange. The point at which it "climbs" the highest is the maximum ordinate. It then drops as the bullet continues downrange, once again crossing the line of sight and continuing to drop as it heads downrange. At another point, it has dropped below the line of sight an amount equal to the maximum ordinate. This distance downrange is the point blank range.
Huh? OK, it just means the distance over which your bullet doesn't drop or rise more than an assumed # of inches (such as 4") above or below the line of sight.
By checking ballistics tables and adjusting your sight/scope, you can set the maximum ordinate to be no more than one-half of the size of the vital zone of your target. For example, you can just sight your .30-06 to hit 2" - 2 1/2" high at 100 and you have a point blank range of about 250 yards (assuming a target with a vital zone of 8"). Military rifles are set up so that the assumed vital zone is bigger and therefore the assumed PBR is longer. They tend to be zeroed for 300 yards. Of course, this means that at very close range, your bullet's likely to sail over the heads of the badguys if you don't apply a little KY windage.
Then, as Art points out it means that distance at which no hold-over is necessary to hit a target.