Although used exclusively in TAS, the life-support belt was invented during the run of Star Trek: The Original Series. Judy Burns, co-writer of "The Tholian Web", thought of using battery-powered "force field belts" in that episode, but the series' producers decided to feature EV suits instead. "They felt strongly that if they started something like a force field belt," explained Burns, "it might have ramifications down the line on other stories. I was a novice in those days, but today I probably would have countered that it was a prototype model that had been given to us this one time. In 25 years, we would get it back again." (Captains' Logs: The Unauthorized Complete Trek Voyages, 3rd ed., p. 72)
In the script for "Beyond the Farthest Star", life support belts are introduced with the description, "The belts are wide, utility-type belts that glow with a pale, lime-yellow aura when turned on. This aura surrounds the wearer, like an envelope of air surrounds the Earth; it supplies air, and being a force-field, prevents harm to the person inside it, as it is almost totally impenetrable."
I always thought that some later uses of the belts, particularly in Slaver Weapon,
were inconsistent with how they were used in Beyond the Farthest Star.
The belts seem to offer some resistance to phaser fire from the automatic bridge defense system, so I always thought they should have stood up better to the Kzinti phasers. I suppose one could posit that the Kzinti phasers were specially modified to penetrate the forcefields.
Also in Beyond the Farthest Star,
Scotty's belt holds up the weight of the Engineering core hatch, which implies that the belts should be able to prevent a variety of objects from penetrating their force fields. Note that Scotty, Chapel, and McCoy use belts underwater in The Ambergris Element
(although it would appear that one of the famous Filmation animation errors resulted in Scotty's belt not being drawn).