It's important to understand that a bullet travels in an arc when it's fired. As soon as it leaves the muzzle of the gun, gravity starts to pull it downward. So the bullet is actually fired upward at a very slight angle. As it travels away from the gun and gravity exerts its pull, the bullet's path is curved, with the concave side of the curve facing the Earth.
The line of sight, through a scope or using iron sights, is a line (and thus is straight). So the trick is to get the line of sight to match closely with the curve of the bullet's path.
In normal sighting conditions, the line of sight will intersect this arc in two places - once when the bullet rises above it, and again as it is falling to earth.
Now - with many high-powered centerfire rifle cartridges, that first point of intersection is very close to 25 yards when the rifle is sighted in for practical hunting use with average ammo. So most boresighting is done to get it close at 25 yards, and when sighting-in a rifle it makes sense to start by zeroing it to hit at point of aim at 25 yards.
After you shoot the rifle at 25 yards and adjust the scope so the bullet hits right where you aim, you can move on out to 50 yards and then 100 yards (or farther) and see how you're doing, and make whatever adjustments are required at those ranges.
For deer hunting, you want most rifles to hit in the center of the target horizontally (side-to-side), and about 1.5 inches above the center of the target vertically (up-and-down) at 100 yards. This usually gives you the capability of aiming at the center of a deer's vitals and hitting within that zone out to 200 yards or more.
This is sometimes called point-blank aim, and a gun's maximum point-blank range is the distance at which the bullet falls below the bottom edge of the imaginary cylindrical tube that illustrates the size of the vital zone of the game being hunted.
- Russ Chastain