Yes, that's approximately what it does. I'm not sure if these values are the exact vertex counts to create, but at least, higher tess factors lead to higher vertex counts. The reason there are separate factors for each edge is so you can match edges from one patch to the next, to avoid cracking.
Here is a video showing the tess factors being smoothly increased on a cube. You can see the effect of fractional tess factors in this video too (how the mesh smoothly and continuously changes from one tess level to the next, rather than popping). It does not show separate edge vs inside tess factors, though.