An antigraviton is a subatomic particle, the antimatter equivalent of a graviton. They can be created artificially, for example as an antigraviton beam, through use of a tractor beam or a deflector array.
In 2370, while examining the transporter logs after Captain Picard and Doctor Crusher disappeared while attempting to beam down to the planet Kesprytt III, the crew of the USS Enterprise discovered an unusual concentration of antigraviton particles in the emitter coil, suggesting that a tractor beam had been used to deflect the transporter beam to a different set of coordinates. (TNG: "Attached")
In 2371, in an attempt to counter an attack by a Vidiian vessel which had grappled onto the hull of the USS Voyager, Commander Chakotay ordered the deflector rerouted to discharge an antigraviton pulse along hull. He then ordered inertial dampers engaged in an attempt to initiate a controlled pitch. The attempt was successful, and Voyager was able to break free of the Vidiians. (VOY: "Fury")
In 2374, Damar developed a procedure utilizing antigravitons to destroy the self-replicating minefield which Starfleet had deployed at the entrance to the Bajoran wormhole in order to prevent Dominion reinforcements from arriving from the Gamma Quadrant. Damar's plan operated by reconfiguring Deep Space 9's deflector field emitter and refocusing the emitters, essentially transforming the deflector array into an antigraviton emitter. The mines would then be isolated in an antigraviton beam, preventing them from replacing themselves. Despite an attempt by an underground resistance movement aboard the station to sabotage the plan, the Dominion was successful in destroying the minefield. (DS9: "Behind the Lines", "Favor the Bold", "Sacrifice of Angels")
In 2375, Yost, supervisor of Renovation Team Nova, attempted to seal a subspace sinkhole in the Delta Quadrant utilizing an antigraviton beam. This forced the crew of Voyager to accelerate their rescue plans for Lieutenant Commander Tuvok, Ensign Tom Paris, and The Doctor, who had been stranded inside a pocket of subspace circumscribed by the sinkhole. (VOY: "Gravity")