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 chitinous, 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 would 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.
That said, a Horadrim Soul Web's impersonation of humanity is not perfect, and a careful observer can notice the telltale signs: Their skin seems stretched and taut, their eyes are spaced a little too far apart, and their mouths are just a little too wide for their faces. Perhaps the most telltale sign is their hair, which they usually wear slicked back along their head, and looks more like part of their scalp than thousands of individual hair follicles (like a department store mannequin). Except for eyebrows, Horadrim in human form also lack body hair - but only someone on very intimate terms with the disguised Horadrim would know that.
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. His former Soul Web was stolen and is now worn by the impostor Emperor, Scyr. After being crippled by a K'Nes-developed software virus supplied to the Federation by Heth, Scyr's Soul Web can no longer maintain coherence, but reverts a liquid mass of pure nanobot soup. The Emperor relies on the power of the Orb to preserve the illusion of normal function.
The Vulthra possess a similar but less advanced technology that can disguise a Vulthra as a human, but each system has a single default human appearance, which is even less perfect a facsimile of a human being than the Horadrim version. The Vulthra version cannot perform any other functions of the Horadrim type, and it has no gestalt mind of its own, functioning purely as a disguise system.
Behind the Scenes
The Soul Web concept, like the rest of the Horadrim, was created by Bax. The malfunctioning liquid state of Scyr's Soul Web is so far seen only in a semi-canonical short story, though it was an attempt to follow a small plot point from Heth's story in Season 9.