(covers information from several alternate timelines)
A feedback pulse is a burst of energy which travels in an opposing direction of pre-existing energy stream, which has the capability of disrupting the initial transmission.
In 2153, Lieutenant Reed and Major Hayes initiated a feedback pulse by reversing polarity on the Enterprise NX-01's plasma coils, in an effort to counter an attack by a Sphere Builder who was attempting to destroy the ship. The plan was successful, and the alien was thrown clear of Enterprise's warp core. (ENT: "Harbinger")
In 2154, a group of Augments left over from Earth's Eugenics Wars initiated a feedback pulse by amplifying a thousand percent a self-destruct command which Hoshi Sato had transmitted to Cold Station 12, which the Augments had taken over. The pulse had the effect of taking Enterprise's communication system offline. (ENT: "Cold Station 12")
In an alternate timeline in 2165, Jonathan Archer initiated a feedback pulse in Enterprise's warp core, in an attempt to trigger a subspace implosion with which to destroy a series of parasites which had infected his hippocampus, impairing his ability to form new long-term memories. As the parasites existed in a state of interspatial flux, existing outside of normal time, destroying them in the present also had the effect of neutralizing them in the past, resulting in the creation of a new timeline in which the infection never occurred in the first place. (ENT: "Twilight")
In 2370, a feedback pulse was created along the particle beam of a phaser beam which the crew of the USS Enterprise NCC-1701-D was using to drill beneath the surface of the planet Atrea IV. The pulse was created as a result of the phaser beam impacting a pocket of magnesite ore, causing the crew to believe that they were going to have to terminate the beam and restart the process in a new location. This proved not to necessary, however, when Juliana Tainer, a scientist working on the project, managed to adjust the phaser harmonics to compensate for the pulse. (TNG: "Inheritance")
The next year, Kathryn Janeway, Voyager's captain, ordered Lieutenant B'Elanna Torres to send a feedback pulse along a tractor beam being utilized by a group of adolescent Borg drones in an attempt to tear Voyager's deflector dish from the rest of the ship. Rerouting warp plasma, Torres was successful, and the pulse successfully overloaded the Borg cube's shield matrix, which drew power from the same grid as the tractor beam. This allowed the Voyager crew to obtain a transporter lock on several of their crewmembers who were being held captive aboard the cube. (VOY: "Collective")
In 2377, an interstellar trader named Gar attempted to use a feedback pulse to destabilize a tractor beam with which the Voyager crew had locked onto his ship. Although Ensign Kim initially attempted to compensate for the pulse, Captain Janeway instead ordered him to simply beam Gar into Voyager's brig, so they could pursue their investigation into the whereabouts of their EMH, whose program Gar had stolen. (VOY: "Critical Care")