Fists are melee attacks available to the player in Doom 3. For most of the game, there is almost no functional reason to use them, because even in the category of non-ammo using attacks, the flashlight does twice the damage per strike, and also provides light. On a per-hit basis, the fists are, however, more powerful than the pistol, albeit with a slower attack rate and limited to melee range.
In the single player story, they become useful when using the Berserker powerup which vastly increases fist damage to the point where even powerful enemies can be killed instantly in a single punch.
In multiplayer, fists can be used to steal weapons from other players.