The Raven Queen, 4E's goddess of death, lives there, and the spirits of the dead head to her little piece of the Shadowfell, Letherna, before they get sent to their final destinations. A lot of 4E Shadowfell material was based around how influential the Raven Queen is, but she didn't make it to 5E's default pantheon. She's super cool though.
The Shadowfell absorbed both the Plane of Shadow and Ravenloft from previous editions. The Mists of Ravenloft (now called "Shadowmist") return to drag evil sons of guns and hapless adventurers into Domains of Dread. The 5E DMG only mentions Strahd von Zarovich and Barovia, but any cool Ravenloft material from previous editions completely fits in the Shadowfell.
The Shadowfell's infectiously dreary atmosphere can have a mechanical effect on PCs. In the 5E DMG this takes the form of a small "Shadowfell Despair" table, but 4E's Shadowfell Campaign Book came with a "Despair Deck" that you could make players draw from when their characters encountered anything especially dreadful. The cards had debuffs (can't make opportunity attacks, -4 to initiative, etc.) brought on by apathy, fear, and madness, and you had to roll a skill check or something during a rest to discard them.
