A paintball is the unit of ammunition used in paintball markers. The standard paintball is .68 caliber, though this tends to vary minutely due to relative humidity and age. Cattlemen used them for years to mark specific members of the herd before the game of paintball came along (and of course, one redneck shoots another and a sport is born). Paintballs come in a broad spectrum in terms of quality, and an even broder spectrum of colors. As with almost all paintball gear, you get what you pay for.
Paintballs are thin-walled gelatin capsules surrounding a colored liquid interior. The paint itself is oil based and is said to come out with water, but it is generally a good idea not to let the stain set in. They are completely water soluble and nontoxic (they are edible, but let me assure you that thet taste like rubber dung), and will biodegrade completely in a matter of weeks if left to the elements. If it rains, they will swell to many times their original size.
Quality paintballs are those that don't have a pronounced seam where the halves of the ball join, and that break consistently on impact and not in the barrel of your marker. Brands that perform well include Diablo, Marballizer, El Tigre, All Star, and Slam. Avoid Brass Eagle (which are funny shaped and break in the barrel) and PMI Big Ball (which are reasonably round but won't break on anything, even a hopper) unless you are short on cash or are just going to use them for practice.