A belt is currently a useless item, and often considered as junk.
Regardless of what may initially seem possible, a belt cannot be worn by the player.
A belt could previously be used in the since removed story mode, where it could be used as a tourniquet for your spouse, Kate.
The health system is rumoured to be improved further at some point in the future, likely giving some usage to the belt, specifically with the return of NPC survivors.
Belts are most commonly found in bedroom wardrobes and shelves in clothing stores. They may also be found in kitchen counters.
From items.txt (Project Zomboid directory/media/scripts/)
Weight = 0.3,
Type = Normal,
DisplayName = Belt,
Icon = Belt,