In simplest terms, the V refers to a Dome's frequency, which you can think of as a measure of its complexity, strength, and roundness. The greater the V number, the more triangles are involved in its construction.
You can watch a quick video here for a visual representation.
The lower the V number, the easier a Dome is to build and manufacture due to more struts being the same length. At the same time, lower V numbers will often look more angular and less typically Dome-shaped. Larger Domes will require increases in frequency when strength becomes more of a factor - this is why our Domes go from 3V to 4V as they increase from 8-9m+.