The primary and most obvious use for a rasp is smoothing. Rasps work much like files or sandpaper applied to carpentry. Keeping a smooth edge on a hoof is critical. This is a matter of structural integrity; sharp edges can catch and chip much more easily, making them more susceptible to damage.
Leveling is the next use. Leveling can smooth out a hoof so that it hits the ground with equal pressure across its surface. Uneven hooves will not distribute the force of the hoof-fall evenly. This can cause damage before the hoof has a change to smooth itself out through usage.
Rounding the hoof is the final most pertinent use of a rasp. Rounding is similar to smoothing. Giving a hoof round edges prevents it from snagging and breaking on impact and also contributes to a more even distribution of pressure and stress. Rounded hooves are better able to absorb impacts. This makes thorough rounding a necessity.
Rasps are very versatile tools. It's difficult to go wrong having a spare on hand. These are not the only things that a rasp can be used for, but they are some of the most pressing needs. Understanding the most common uses of a rasp will make it easier to select one from a supplier.