If we're talking BORE as in barrels (as opposed to boar as in wild pigs), then.....
Paintballs are all supposed to have a diameter of 0.680 inches. In reality paint is hardly ever that small - the size will vary between makes + between different batches of the same make.
If you had a barrel with a bore size of 0.680, then I doubt you'd ever get a single ball out of it, so barrel manufacturers offer barrels in different bore sizes - allowing you to find a barrel which fits your paint.
You can either buy a number of different barrels with assorted bore sizes, or get a kit with interchangable backs or inserts which does the same job. I use a Powerlyte Scepter kit which comes with 5 different size inserts - 0.684, 0.686, 0.688, 0.690, 0.692 - at the start of the day you just select the insert which best fits the paint you're using and you're away.