Andy,
As soon as a bullet leaves the barrel it begins dropping due to the forces of gravity. The term flat shooting generally refers to a cartridge which drops a small amount within a defined range of distance. The rate of drop varies with the ballistic properties of the bullet (ballistic coefficent) and velocity.
The line of sight crosses the path of the bullet at 2 points in space. The first point is at close range and if drawn on paper gives the impression that the bullet actual rises before beginning to drop. The 2nd point is at a greater distance and if drawn on paper is where the bullet again crosses the line of sight as the bullet drops. The idea of being able to sight at 25M and be on target at some greater distance do to this alignment of a straight line (the line of sight) and the curved path of the bullet intersecting the line of sight at 2 points in space.
As Steve Smith has said, that is why sights adjust so you can alter those intersection points in space.
Problem with using a red dot scope with say a 4MOA dot for accuracy shooting is that dot covers a large area that increases with distance, not a problem for hunting at 25-200 yards, but a big problem beyond that. A scope with a fine crosshair and a 1/8 MOA dot is preferred for precision shooting. To give an example of the difference, at 600 yards, a 4 MOA dot would cover a 24 inch circle on the target where a 1/8 MOA dot would be less then 1 inch. For my shooting, I have 2 scopes, a 16X and a 32X. I use the 32X actually at shorter ranges and the 16X at longer ranges.