The Shadowfell is a mirror of the Material Plane, albeit a heavily distorted one; think of how a tree looks vs the shadow of that tree at various points during the day, or looking at the world in a funhouse mirror. Some points are very, very similar, such as the Aegis Islands where there is a portal between the two planes, and the capital cities of Broumov and Vomor, as well as a few other places. Other portions are completely different. Even time generally moves differently in the Shadowfell.
The Shadowfell has been under the jurisdiction of Jenova, the Lady of Shadow, for roughly 500 years. Before then, it was controlled by Lolth, the Spider Queen. During the Harbinger Coup, Cyric aided Lolth in reclaiming the Shadowfell by imprisoning Jenova. This was reversed when the Sandstriders removed the ancient gem from the altar in the capital city of Broumov, and Jenova reclaimed the realm soon after.
From the Shadowfell, one can access the Material Plane and the Underdark.