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.
The Realm of Shadows may be the same World of Shadows as the one that becomes visible when a [Elixir of Shadows] is consumed. It may also have something to do with shadow magic and shades. Death knights, necromancers, and undead as a whole share a strong connection with the Realm of Shadows from many hints that can be seen in-game. In the death knight starting zone, death knights are given the task to enter the Realm of Shadows in order to gain their Deathcharger. Later on, death knights are eventually able to learn the ability [Raise Ally] which pulls their ally's spirit back from the Realm of the Dead and forces it back into their body. Upon doing so, a buff is applied to the player stating that: "A touch of the spirit realm still lingers..." This shows that death knights and necromancers both have a connection to the Realm of the Shadows/Dead to perform necromancy which furthers the idea that they actually are drawing their magical power from it.
The Shadowlands can be seen as a shadowy version of the physical world, and can be routinely visited as a spirit when player characters die. Governed by the Covenants, the four ruling realms of the Shadowlands are Bastion, Ardenweald, Revendreth and Maldraxxus (although countless others exist), which serve as the main setting of World of Warcraft's eighth expansion.