A graviton stabilizer is an important part of a Starfleet ship's artificial gravity system. This stabilizer modulates the level of gravity produced, and if it fails, it could pull too hard and make a person feel ten kilograms heavier.
In 2375, the Defiant's graviton stabilizer was damaged, and Captain Sisko gave Chief O'Brien three days to fix it. O'Brien then gave the responsibility of finding a new stabilizer to Ensign Nog.
While the USS Sentinel was visiting Deep Space 9 about the same time, they had a surplus graviton stabilizer. Nog procured this in a series of trades. (DS9: "Treachery, Faith, and the Great River")