Compressors actually reduce volume, hence the term "gain reduction". By reducing certain aspects of a signal you are, in turn, leveling louder parts with the quieter parts. When you bring the gain back up, which is referred to as "makeup gain" (the compensation for the gain LOST in the process of compression), if done right, it would have a thicker, possibly louder apparent volume. Before I go off on a tangent and start making absolutely no sense, I will post this link to a thread that was right on the same page you posted this thread. The compression horse has been beaten to death on this site, so here it is:
Compression Basics

