The shell of paintballs is almost invariably constructed of gelatine. Think of them something like a large supplement capsule, the material holds the fill in well and will break with a heavy impact. Say, being propelled by a CO2 burst into your mask.
The origin of paintballs is a little bit less safe: they were constructed of thin glass. However, these were used primarily to mark cattle and trees and weren't used for the sport.
Gelatine has a number of interesting properties, but the main one that will concern most players is the fact that when dropped it has a tendency to absorb water. This can cause swelling with even a limited amount of contact time.
Swelling can cause jams in your marker, or cause the ball to break in the barrel which results in one heck of a mess.
Basically, if you've dropped your paintball… let it go. Recovering it might seem economical, but once they've hit the ground you really don't want to use them anymore.
You'll also want to keep them out of the sun and from prolonged exposure to air. This can cause the gelatine to harden, which means that you won't get a satisfying splat when you hit your opponent and will instead have to rely on them noticing the hit.
This over-drying can also cause deformation of the paintball, leading to breakage in your barrel and affecting the accuracy of the shot.
Because of this, many players buy their paintballs early before their next time in the field. You simply don't want them sitting in the open for too long or they'll “go bad.”