Adventurers entering the Shadowlands will find the realm of the dead in disarray. In the natural order of things, souls are sorted and sent on to an afterlife realm appropriate to the lives they lived, but starting around the time of the Burning Legion's third invasion of Azeroth, all souls who have perished—including the innocents slain at Teldrassil—are being funneled directly into the Maw. The Shadowlands are starving for anima even as the Maw continues to grow from the glut of fresh souls. Sylvanas Windrunner has been seemingly perpetrating acts to bring about great amounts of death and destruction. In partnership with the Jailer, they have been working toward a common end for some time.
Covenants grant two additional gameplay abilities, one being class-specific. It alters your playstyle. Covenants grant unique armor styles and special capes that look a little more like accessories. Titan-like Kyrian capes look more like angel wings, for example. Each Covenant has a unique campaign similar to those found in Battle for Azeroth and Legion.
In the opening cinematic, Sylvanas shatters the Helm of Dominion, breaching the veil between the material realm and the Shadowlands, an ancient dimension where the dead coalesces for judgment. Sylvanas' actions have upset the natural balance between life and death, and it's on players to enter the Shadowlands itself and repair the cycle before it is too late.
Claim a covenant's power: players will be called upon to forge a bond with one of four covenants that rule Shadowlands' new zones, setting the tone for their journey through the expansion with a full covenant campaign. As they level up, they'll get new abilities based on their choice, including class-specific abilities for each Covenant—as well as developing soulbinds with specific covenant members, which grant them access to that character's specific traits and bonuses.
The Shadowlands were originally intended to be a fully playable zone in World of Warcraft, designed for high-level play. The idea was that as deceased characters made their way back to their corpses, they'd see high-level players battling creeps in the area, which would inspire lower level players to increase their character level so they could experience the zone for themselves.
Shadowy Tormentors inhabit this dimension, and emerge from it to torment death knights such as Koltira Deathweaver. The Lich King originally kept them at bay, but after the Knights of the Ebon Blade left his service, the tormentors are now loose upon them. He even appears in the World of the Dead, as he calls it, riding a frost wyrm during  The Power to Destroy.