A temporal stabilizer, also known as a temporal discriminator, was a device that stabilized a wearer's existence in a single timeline, and could also prevent the wearer from experiencing time alterations made to the timeline.
Starfleet
In 2384 aboard the USS Voyager-A, The Doctor built a temporal stabilizer, based on improvisation with a phase discriminator, in order to keep Gwyn from bouncing between different quantum timelines due to a temporal paradox. The Doctor warned Gwyn that it was only a temporary solution, and also not to fiddle with it. The Doctor's version was worn as an armband and displayed single digits of a number representing the current quantum frequency it was set to. When a mysterious entity contacted the USS Protostar crew via Murf, Gwyn intentionally fiddled with her temporal stabilizer, despite her friends' protests that the stabilizer was the only thing keeping Gwyn in their own reality. Gwyn changed the stabilizer's frequency in order to follow a clue that would lead them all closer to fixing the temporal paradox. (PRO: "Temporal Mechanics 101", "Observer's Paradox")
When Gwyn's temporal stabilizer was damaged on an away mission, Rok-Tahk was able to fix it using only tools on the Infinity. (PRO: "The Fast and the Curious")
In the time ziggurat, when Wesley Crusher saw Gwyn's temporal discriminator, he very much wanted to improve upon it, but reminded himself that The Doctor's version was working just fine and he had other problems to deal with. (PRO: "The Devourer of All Things, Part I")
When an away team from Voyager beamed down to the time ziggurat, The Doctor sent them with an improved version of his temporal discriminators, in case time were to get unusual on the surface. This was fortunate, since the away team was attacked by the Loom, cosmic scavengers who fed on dying timelines by freezing time. When time began to gradually freeze, Commander Tysess tapped on both his discriminator and Maj'el's to activate them both to fully counteract the time slowdown. The Doctor began manufacturing more temporal stabilizers, but not nearly enough for the entire crew of Voyager to resist the Loom. (PRO: "The Devourer of All Things, Part I")
After recovering the Protostar, as they dropped out of proto-warp to approach Voyager-A, Gwyn's temporal stabilizer began to glitch, and Gwyn felt faint like when she was first suffering from the temporal paradox. When they beamed over to Voyager, they discovered that their proto-warp had fractured reality, and different sections of the ship existed in different realities. Each time Gwyn passed to a different reality within the ship, it affected her more and more. When they ended up in the mirror universe and the Loom appeared, Gwyn's temporal stabilizer again prevented her time from freezing, allowing her to complete their plans to escape back to their own reality. (PRO: "Cracked Mirror")
Gwyn was finally able to remove her temporal stabilizer after the Protostar and Voyager-A crews successfully opened a wormhole and sent the Protostar back to its proper place in the timeline, fixing the temporal paradox that the stabilizer was protecting her from. (PRO: "Cracked Mirror")
Travelers
Traveler Wesley Crusher used a different design of temporal stabilizer than Starfleet, one that was worn as a bracelet on the wrist (though he still referred to it as an armband). In 2384, Wesley provided stabilizers of this design to the Protostar crew so that they could all escape from the Loom's ability to freeze time. Foreseeing that his gadgets would be needed, Wesley had stashed the stabilizers in the time ziggurat so that he could provide bracelets sized appropriately for each of the Protostar crew members when they arrived. (PRO: "The Devourer of All Things, Part I")
Though the temporal stabilizers had kept them all safe from the Loom, neither the crew's stabilizers from Crusher nor Maj'el's stabilizer from The Doctor passed through the portal to Ysida with them. Gwyn's stabilizer did pass through with her, since it was the only thing keeping her in existence. (PRO: "The Devourer of All Things, Part II")