Nobody has yet mentioned the basic physics here, so I will; forgive me if you knew this already.
Scratches, cuts, or abrasions of any sort on a ball will cause it to curve unpredictably, especially when pitched. Baseballs are very prone to curving downwards or to one side due to imperfections on the ball’s surface. Pitchers can legally use this effect by throwing the ball so that the rotation of the seams causes a variety of nasty, hard-to-hit effects such as a downward curve or drop (curveballs and forkballs) or a left-to-right curve (sliders, screwballs, fastballs.) This is especially pronounced at the major league level, where the pitches are thrown extremely fast and the effect of cuts on the ball’s surface will be most pronounced. In fact, pitchers have been known to deliberately deface the ball using emery boards and hidden blades. This practice is against the rules, by the way, and would result in ejection from the game. Prior to 1920 it was permitted.
Consequently, it is always to the hitter’s benefit to ask that a clean ball be put into play. The umpires generally try to never have a scuffed ball in play, since it’s unfair to the hitters and potentially dangerous.
Pitchers will also sometimes ask for new balls if they don’t like the fell of the old one. Baseballs, as manufactured, are unsuitable for major league play, as they are too slick to pitch. Prior to major league games, the umpires rub down the baseballs with a small amount of (specially produced, allegedly taken from the banks of the Delaware) mud, just enough to get the sheen off the ball and give it a good grip. Some are better rubbed down than others, so if a ball doesn’t have a good enough grip you’ll often see the pitcher throw it back and ask for another.