The Soul Cairn is one of the many planes of Oblivion. Inside on the realm, the undead are able to roam free, and the souls captured in Black Soul Gems stay trapped for all eternity. Rather than belonging to a Daedric Prince, it is controlled by a group of beings known as the Ideal Masters.
Little to nothing is actually known about the Ideal Masters; what they are, where they came from, or what they even look like is all up for debate. At the time of Dawnguard, Serana and the Dragonborn must enter the Soul Cairn in order to find Valerica, who will give them an Elder Scroll so that they can gain the knowledge of where to find Auriel's Bow.
According to Valerica, many Necromancers make deals with the Ideal Masters in hopes of getting immense necromantic power. Unfortunately, these Necromancers are usually tricked by the Ideal Masters and end up trapped in the Soul Cairn forever. Why this happens is mostly unknown, but it is safe to assume that so the Ideal Masters can have access to their souls.
While exploring the Soul Cairn, the Dragonborn may find the soul of Jiub, from The Elder Scrolls III: Morrowind. He says how, during the siege of Kvatch by the forces of Mehrunes Dagon in the Oblivion Crisis, he was attacked by a Dremora who trapped his soul into a Black Soul Gem. Jiub gives the Dragonborn the quest Impatience of a Saint after he states how he was almost done with the second part of his life story, and how he lost the notes for it once he entered the Soul Cairn.