From The Straight Dope:
Of course, working out more doesnâ€™t reduce pain and stiffness (often called delayed onset muscle soreness, or DOMS) â€“ if anything the opposite is true. Since lactic acid dissipates within an hour of exercise, something else must be causing pain the next day. The current thinking is that the something is plain old water. Working out causes tiny tears in the muscle fibers into which water infiltrates. That causes stiffness, the way a balloon filled with water is stiffer than an empty one, and soreness, by pressing on nearby nerves. This process is commonly known as inflammation.
It seems logical that massage wrings water and salt out of the muscles and increases local circulation so that the excess is carried away in the blood and excreted. Drinking extra water is probably useful only if youâ€™re dehydrated and isn’t directly involved in reducing pain and stiffness. According to a 2005 review in Sports Medicine by Pornratshanee Weerapong and colleagues, research support for this theory is inconclusive, but for the sake of argument we’ll assume it’s possible.