(covers information from several alternate timelines)
The transphasic torpedo was an advanced type of torpedo weapon of unprecedented destructive potential used by Starfleet. The torpedoes could be launched from standard starship-mounted torpedo launchers. A single torpedo was capable of destroying a Borg cube. This weapon technology was acquired by the crew of USS Voyager in 2378 from Admiral Kathryn Janeway of an alternate timeline. (VOY: "Endgame")
In the alternate timeline, this weapon system was developed as an anti-Borg technology by Captain Janeway. The torpedoes were invented some time after they encountered the transwarp hub hidden inside a nebula in 2378, but chose not to investigate it further. She used the technology to defend Voyager against the Borg on their voyage back to Earth. In 2404, Admiral Janeway embarked on an illegal mission to change history by traveling back in time through a temporal rift to secure Voyager's safe return to the Alpha Quadrant sixteen years early.
Arriving to 2378, Admiral Janeway brought the advanced technology with her on the shuttlecraft SC-4, and shared the technology with the crew of Voyager along with ablative generator-technology. Admiral Janeway assisted the crew in upgrading the torpedoes carried by Voyager, turning them into transphasic torpedoes. The torpedoes subsequently proved extremely effective at combating the Borg vessels guarding the transwarp hub in grid 986, allowing the crew to destroy two cubes. They also used the torpedoes to blow up a Borg sphere, that had captured Voyager into its internal bay.
Voyager used transphasic torpedoes to destroy the interspatial manifolds supporting the structure of the hub, causing the Borg's transwarp network to collapse. The manifolds though weren't as vulnerable as Borg ships, as their shielding was regulated from the central nexus by the Borg Queen, which would have allowed the collective to adapt to the transphasic torpedoes after a few of the manifolds were destroyed. Admiral Janeway was however able to kill the Queen with a neurolytic pathogen in time to allow the plan to succeed. (VOY: "Endgame")
According to the Pocket Books novel Greater than the Sum, transphasic torpedoes were in fact kept by Starfleet as the weapon of last resort to be deployed to starships only when all else had failed against the Borg. They were the one and only thing Starfleet knew the Borg had not yet adapted to and for that reason wanted to keep this ace in the hole for as long as possible. As a result, during the subsequent Borg invasion in 2380, the USS Enterprise-E was the only Federation ship equipped with transphasic torpedoes, engaging in rapid hit-and-run missions to limit the Borg's opportunities to adapt to them.
The warhead technology of the torpedoes was also revealed in the novel. It is based on generating a destructive subspace compression pulse. Upon detonation the torpedo delivers the pulse in an asymmetric superposition of multiple phase states. Shields can only block one subcomponent of the pulse. The other subcomponents deliver the majority of the pulse to the target. Every torpedo has a different transphasic configuration, generated randomly by a dissonant feedback effect to prevent the Borg from predicting the configuration of the phase states.
In the novel Lost Souls, set in 2381, during a Borg invasion, the Borg finally adapted to the transphasic torpedoes when Starfleet was forced to send the torpedo specs to the entire fleet following a mass incursion of Borg cubes. According to Gods of Night, set in the same year, the transphasic technology of the torpedoes could be applied in deflector shields also to create transphasic shielding and to phaser technology as well, although the phaser application was not powerful enough to be effective.
In the novel Headlong Flight, the Enterprise-E makes contact with a version of the Enterprise-D from an alternate timeline where, among other differences, Picard died during the Battle of Wolf 359 and Riker has been captain of the Enterprise for a year. Recognising the complex nature of the current encounter in terms of the proper application of the Temporal Prime Directive, but equally aware of the danger of the Borg, Picard provides the alternate Riker and his crew with information on how to create transphasic torpedoes for themselves before the temporal rift that allowed them to travel between universes is repaired and the two ships return to their own realities.
In the game Star Trek Online, set in 2409, transphasic weaponry is used by several races, mainly by the Breen and Hirogen, in regular combat, and not only against the Borg. Transphasic weapons, usually employed in torpedo or mine form, are not nearly as destructive as depicted in Star Trek: Voyager, but are instead only distinguished by their ability to penetrate a target's shields. In season 9 of the game, adaptive transphasic torpedoes were introduced as a unique mission reward. They increase damage against Borg ships.