The salt does 2 things. First is related to osmosis. Because the brine is saltier than the fluids in the meat, it initially draws moisture out of the meat. However, once an equilibrium is reached and the fluid in the meat and the brine are the same salinity, moisture can pass back and forth between the meat and the brine. When this happens, any flavoring agents you have put into the brine are carried into the meat, so you can add flavor to the meat with brining.

The second thing the salt does is it denatures the proteins in the meat which allows the proteins to trap moisture in the meat. So, while the brining process actually removes some moisture from the meat, the result is that the meat holds on to the remaining moisture with a vengeance. Thus the net result is that the meat gives up less moisture during cooking and you end up with more moisture in the meat than if you had not brined, even though brining removed some moisture to begin with.