Exterior ballistics is the study of how bullets behave between the muzzle and the target.
Bullets have two things working against them: air and gravity. Air resistance makes them slow down, gravity makes them fall. This means that bullets don't travel in a straight line. They travel in a parabolic arc. The good news is they behave (pretty much) the same from shot to shot.
Light does travel in a straight line (more or less, most of the time).
So, since the sights are usually above the barrel, and since light travels in a straight line but bullets fall, if the sights are parallel to the barrel the bullets always hit low.
The solution is to have the line of sight converge with the line of the barrel. The bullet will cross the line of sight twice; once on the way up, and once on the way down. The sights will be right on for a target at either intersection.
The angle between the line of sight and the bore of the firearm is called the sight angle. The sight angle in the graphic above is exaggerated for clarity. Adjusting the elevation of your sights changes the sight angle.
The place where the line of sight and bullet path intersect at the target is called the zero. For example you might say "My rifle is zeroed at 200 yards." Changing the sight angle changes the zero.
The near zero is where the bullet path crosses the line of sight the first time. The zero and the near zero move in opposite directions as you adjust your elevation. If you zero your gun at a more distant range the near zero will get closer to you. As you bring the zero closer to you the near zero moves away from you until they converge.
The point where the bullet path is the highest above the line of sight is called the midrange. This is not halfway to the target. Midrange is closer to the target because as the bullet slows down it falls at a steeper angle.
Point blank range is the maximum range at which you can hit a target of a specified size without a sight adjustment. Many people use the term "point blank" to mean "really close", but with respect to ballistics it doesn't mean that.
Suppose you are hunting deer. You know where you want your shot to hit, but you have determined that any shot not more than 4" high or low is acceptable. The point blank range is the maximum range for which this is true.
What sort of things affect external ballistics?
Note: The ballistic coefficient, BC, is a measure of how much bullets are affected by air resistance. Higher numbers mean the bullet is less affected. Factors that influence BC are caliber, weight and shape.
Although bullets with the same BC follow the same trajectory for a given muzzle velocity, their terminal performance (how they behave on impact) still depends on caliber, weight, shape and other design factors.
Now that you have your favorite gun and ammo all sighted in, what will cause your zero to change?
The estimates in parentheses are for a bullet with a BC of .4 and a MV of 2700.