Dry aged carcases are hung in a cooler at high humidity. During this time natural enzymes and bacteria in the meat do their thing and tenderize the meat. As mentioned, there is some loss of moisture within the meat. Also, the outside of the carcass gets moldy, ugly, and nasty looking.
Dry aging is expensive because of the costs involved in storing the meat for a couple of weeks, then you have to pay someone to cut all the mold off (losing some of the meat in the process), then you have to pay someone to butcher it.
Wet aging costs a lot less because you just slaughter, butcher, cryovac, and ship, plus you don't lose any meat to mold.
I've had dry aged beef and can't understand how a person could prefer wet aged, but supposedly some people do.