It is a generalization derived from several items, primarily high velocity (which lets the bullet travel farther during a given amount of time) and favorable ballistic coefficient (which lets the bullet overcome air resistance thus staying faster, longer).
A bullet that doesn't move very fast and which slows down quickly (say a mild .45-70 load) must be fired at a relatively sharp initial upward angle to account for how much time the bullet needs to get where it's supposed to go. If a bullet will take (for the sake of discussion) 2 seconds to cross a given distance, it is going to fall downward something like 96 feet before it hits. *** So you'll have to aim the gun upward enough to launch that bullet 48 feet above the target at roughly the midpoint (actually a bit past the midpoint) of its trajectory. If it left a trail in the air you could see, it would look a little like a rainbow.
(*** Anything dropped or thrown falls towards the earth at a rate of acceleration about equal to 32 feet per second, per second. Thus, 32' in the first second, 64 additional feet during the second second, 96 feet in the third second and so on.)
If, on the other hand you fire a bullet a lot faster and it doesn't slow down as fast because it has a good "BC," (lets say this is a .220 Swift, or a .260 Remington or a .338 LM or other pretty zippy round), maybe that bullet will cross the same distance in only one second. If that's so, you'll only have to point your rifle barrel high enough that the bullet will be about 16' above the target at the midpoint of its path. It is still going to fly in a rainbow or arc parth, but a much flatter one.
Hence a "flatter" trajectory.
Said another way, if you watch a quarterback throw a football to a receiver, he throws it way up in the air and the receiver catches it as it comes back to earth. If you watch a 3rd baseman throw a baseball to 1st base, it will almost appear to follow a straight line. A person can't throw a football as fast as a baseball, and it's bigger -- creating more drag and slowing down faster. To get it to fly the same horizontal distance you have to aim it pretty far up in the air. The baseball has a "flatter" trajectory.
Make sense?
(Yes, the numbers are mighty rough. Shouldn't need a ballistic chart to explain the principle, I don't think.)