dont let what dgallo said confuse you. carbonation is simply and only temperature and pressure. the rest of the stuff hes talking about is for draft systems, not carbonating your beer.
a volume is simply that, a volume. if you have a 5 gallon keg full of beer, then 2.5 vols co2 means you have the equivalent of 12.5 "gallons" of co2 in it. (5 x 2.5) its basically a measurement of how much co2 is dissolved in the beer.
the carbonation charts will ususally give you an idea of how many volumes are typical or appropriate for a style of beer. if you're bottling, then follow the advice of an online calculator to tell you how much sugar to prime with for your batch. if you're kegging, then you use the chart to match your keg's serving temperature to the volumes of co2 you want, and that will tell you what psi to set your regulator at.