"Punch when not equipped"
When equipped, the Fist Ring will allow Link to attack with his fists. As long as Link does not have an item equipped in either the 'A' or 'B' button slots, Link will punch when the corresponding button has been pressed. Link's punch when holding this ring does half the damage as that of the Wooden Sword.
The Fist Ring is nearly identical to the Expert's Ring. The only difference is that the Fist Ring is significantly weaker than the Expert's Ring. Considering it does less damage than the Wooden Sword, there is absolutely no practical use for the Fist Ring. The only use for it is to make the game more challenging, similar to other custom game challenges such as a Three Heart Challenge.