The Vengeful Spirit is the Gloriana-class battleship that served as the flagship of Horus Lupercal during the Great Crusade and the Horus Heresy. Currently, it is under the command of Abaddon and serves as the flagship of the Black Legion when he's not riding in a Planet Killer or Blackstone Fortress.
One of the few Gloriana-class ships ever built, the vessel acquired a fearsome reputation during the Great Crusade, which only increased during the Heresy. By the time of the Siege of Terra, the ship was essentially a space-borne temple of the Chaos Gods. The final confrontation between Horus and the Emperor took place on the corrupted bridge of the ship.
Ezekyle Abaddon took command of the Vengeful Spirit during the retreat from Terra, and proceeded to fly it deep into the Eye of Terror. Somehow, he managed to get it through the huge, permanent, destructive storm of psychic fire that surrounds the "Radiant Worlds" and hide it on an old Eldar world while he went into an emo phase and wandered aimlessly around the Eye.
Upon learning that Fabius Bile had cloned his father, Abaddon finally ended his gap century and, with a skeleton crew of Chaos Marines who would become the Black Legion, used the vessel to utterly destroy the Emperor's Children at the Battle of Harmony. Since then, he has used it as his personal flagship. While the Planet Killer briefly displaced the Vengeful Spirit as the Black Legion's flagship during the Gothic War, the destruction of the Planet Killer saw the Vengeful Spirit retake its place at the head of the Black Legion's fleets. The vessel was confirmed to be part of the Traitor Fleet that attacked Cadia during the 13th Black Crusade, and was the vessel Abaddon escaped to when Cadia was destroyed. Presumably, the Vengeful Spirit is now leading the Black Legion fleet on a rampage through the galaxy.
In case anyone read the Iskandar Khayon section, they would know that the Vengeful Spirit had a machine spirit named Anamnesis, that was created from the brain of Khayon's sister Itzara. It used to belong to one of the old Thousand Sons vessels known as Tlaloc. When Khayon found the Vengeful Spirit, he decided to claim it as his own by installing Anamnesis onto it and psychically thrown Anamnesis's "old body" towards Emperor's Children's main stronghold and destroy it (because he fucking hates those pink bastards for being a bunch of noobs during the Siege of Terra). Effectively it means the Spirit needs less of a crew since the Anamnesis links directly or is fused to the Machine Spirit of the ship. In battle the crew is shown to help though, and Itzara does not replace a Navigator or Voidseer.
In Battlefleet Gothic
The Vengeful Spirit appears in Battlefleet Gothic as Chaos Battle Barge that had the option to be led both by a Chaos Lord and embark Chaos Space Marines on it. If the latter option was taken, it could also take Chosen Chaos Terminators for more effective boarding/hit and run attacks.
That little bit aside, it's no more powerful than your usual Chaos battle barge (not even additional defenses or weapons), which is a bit of a let-down considering its reputation and history.
In Battlefleet Gothic: Armada 2
The Vengeful Spirit appears as Abaddon's flagship for this game, replacing the Planet Killer (which was loaned to one of his Chosen and the Iron Warriors) that was used previously. It serves as the final "boss" of the Imperial campaign.