A Soul Web is the network of gestalt-intelligence nanotech-based entities which reside in the bodies of Horadrim and human-Horadrim Hybrids and give them most of their special powers. Also sometimes referred to as a Life Web.
A Soul Web allows a Horadrim to shapeshift their own body, extruding temporary pseudopods or tentacles with sensors such as temporary eyes, or olfactory organs or even taste buds, to explore the environment around them. In its most extreme form, it allows a chitonous, insect-like Horadrim to appear almost indistinguishable from a human being, by shifting their entire body so much that they take on human appearance. Individual cells are pulled apart by the nanobots, rearranged, and put back together in the new shape. While this woudl technically allow a Horadrim to take upon almost any human appearance they like, in practice most of them settle upon one human appearance and identity.
Like other Human-Horadrim hybrids, the Emperor has a Soul Web. This makes Soul Webs in general an object of veneration amongst adherents of the Cult of the Emperor, and many of the more fanatical amongst them would gladly kill to obtain one if they didn't hold other Horadrim and hybrids in similar religious awe as angel-like figures. Unbeknownst to them, Emperor Vin Dane is dead, and his former Soul Web, crippled by a K'Nes-developed software virus supplied to the Federation by Heth, has been stolen and is now worn by the impostor Emperor, Scyr. Due to degredation caused by the viral weapon, Scyr's Soul Web is malfunctioning and must periodically be separated from his host body to repair and regenerate itself as a liquid mass of pure nanobot soup.
The Soul Web concept, like the rest of the Horadrim, was created by Bax. The liquid regeneration state of Scyr's Soul Web is so far seen only in a semi-canonical short story, and is likely inspired by Odo's need to similarly regenerate in a liquid state on DS9.