This is the amount of damage added to the upper end of hand-to-hand and melee attacks. It is possible to have a Melee Damage of 5 and still do only one point of damage when you attack, based on armor and the fact that this stat adds to the maximum amount of random damage done, not the minimum. If a weapon does 1-4 points of damage (which you can see on the inventory screen), and your character has a Melee Damage of 2, that weapon would do 1-6 points of damage before being modified by the armor of your target.