Yes, you got it. One volume of CO2 means that their is one liter of air dissolved into 1 liter of liquid. The reason everyone uses the volumes system is because of the variables of temperature and pressure that go into the equation. Two kegs can both have beer stored at 2.5 volumes of CO2, with one keg at 37 degrees and under 11 psi while the other could be at 60 degrees and 23 psi. Volumes, like gravity units for example, is a common unit which takes into account multiple variables.
The key with understanding volumes is that certain beer styles are mean to be served at different volumes of CO2. For example, some English Ales are served at 2.0 volumes of CO2, American Ales at 2.5-3.0 volumes, and Belgian Ales can be as high as 3.5-4.0 volumes. That is a big difference in terms of carbonation level and mouthfeel for your beer. There a lot of good resources you can refer to which will give you the suggested carbonation level based on that BJCP style. I believe you actually can find those suggestions on the BJCP site itself under each individual style.
