The Unarmed skill is used for fighting without a weapon, or with weapons designed for hand-to-hand combat, like Brass Knuckles, Power Fists, and Displacer Gloves.

The other melee skill, Unarmed has a bit more going for it than Melee Weapons. For one, a high Unarmed skill is required for both the Slayer and Piercing Strike perks, both of which are obligatory for melee-type characters. Power Fists can be found pretty readily at Camp Golf, and even Spiked Knuckles tend to out-perform low-end Melee Weapons. Also, the fact that most builds call for high Endurance plays into the Unarmed skill right from the start.