These boots provided stability by adhering to a compatible surface, useful when sufficient gravity (or artificial gravity) was not available, including extra-vehicular environments ("space walk" situations).
In 2063, Captain Jean-Luc Picard, Lieutenant Commander Worf, and Lieutenant Hawk all wore gravity boots while on the hull of the USS Enterprise-E so they could destroy a Borg interplexing beacon located at the ship's navigational deflector. (Star Trek: First Contact)
In 2293, Yeomen Burke and Samno wore magnetic gravity boots to assassinate Chancellor Gorkon, while artificial gravity was knocked out on Kronos One. Lieutenant Valeris later stowed one boot in Crewman Dax's locker to implicate him in the assassination. (Star Trek VI: The Undiscovered Country)