Spoiler warning: Plot and/or ending details follow.
A transwarp conduit, also known as transwarp corridor or a transwarp tunnel, is an artificial construction that allows travel over great distances. The opening of a conduit is known as a transwarp aperture.
Between 2373 and 2374, the Borg created a transwarp conduit to the Gamma Quadrant in preparation for an invasion of the Dominion. Their early attempts were stymied by an attack on the assimilated USS Valkyrie by the Jem'Hadar and the emergence of Species 8472 in the Delta Quadrant. (DS9 novel: Lesser Evil)
In 2380, an assembled task force of Federation, Klingon and Romulan vessels attempted to hunt down and destroy the rogue Vulcan T'Uerell who had attempted to form a Borg Collective of her own which used logic to bring about order. They discovered that she had harnessed the power of a polaric ion energy string to help power a highly stable transwarp conduit in order for her to bring reinforcements to protect her. Admiral Kathryn Janeway commented that this conduit was different from the ones she encountered and was unusually stable as it was being directly controlled by T'Uerell using the power of the string to keep it open. This conduit was destroyed once the Vulcan and her starship were destroyed. (ST video game: Legacy)
By the 2390s, the Federation was again experimenting with transwarp conduit technology, based on Borg designs brought back from the Delta Quadrant by the USS Voyager. In 2399, the first links of the Federation Transwarp Network were established, making fast travel between distant star systems possible. (ST website: The Path to 2409)
In the 3180s, Starbase 906 was in charge of project to use transwarp conduits as alternative to warp due to The Burn. In 3186, the White Palm took control of both the Starbase and accessed the project. Despite the technology's instability, White Palm was able to gain an advantage.(DSC novel: Wonderlands)
By the late 3180s, several conduits were used by couriers. However, the conduits were strewn with debris from The Burn and few would take the risk. However the Emerald Chain's minister Ossyra would take the Viridian to capture the USS Discovery-A near the Verubin Nebula. Commander Michael Burnham and Cleveland Booker would take his scout ship through the conduit to board the Discovery.(DSC episodes: "Su'Kal", "There Is A Tide...")