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.
But it gets even more interesting when you look at how it will work for alts (second or later characters made by existing players). New characters made by existing players will have the option of leveling up the old way in all the same old zones from the start. But they will also be able to go through the new-player starting experience if that's what players prefer.
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.
Blizzard's new solution in Shadowlands is to return the level cap to its original value of 60 and to make current content appropriate for levels 50 through 60. New players start at level one, and they all play through a new introductory zone built for Shadowlands based on the quest design lessons Blizzard has learned over the years. Once they play through that introductory experience, they can then level up to 50 to catch up with current content by playing through the previous expansion (Battle for Azeroth) right away (from around level 10).
It's hard to get a sense of an entire World of Warcraft expansion from 30 minutes of play. In my short demo, I recreated my main (a Beast Mastery Hunter) and played through the introductory quests from the Bastion zone, a heaven-like plane from Azeroth's afterlife. The minute-to-minute gameplay very much followed the formula of modern WoW questing, with a variety of tasks like challenging specific enemies to duels, helping craft things in timed minigames, and of course, killing 10 rats (well, not rats, but they might as well be).
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.
The origins of the Shadowlands remain uncertain, but they have existed ever since mortal life first arose in the physical universe. They span all worlds, including Azeroth, on which Icecrown serves as an anchor to the Shadowlands. There are those who believe mortal souls are drawn into this dark place when they die, remaining there forever. Others hope their souls will go on to a brighter place rather than languish for eternity within the cold confines of the Shadowlands.