A lightsaber shroud is an overlay or a piece that covers up part of the main body of the lightsaber hilt. Sometimes a shroud will cover a lot of the lightsaber hilt and sometimes it will only cover part of it. The only real requirement for a shroud is it must serve as an overlay to the lightsaber hilt.
Sometimes a shroud covers a large section of the lightsaber hilt body. On The 7 Chambers Phoenix Props Imperial Knight (second hilt from the right), the a shroud encases the black body of the hilt, covering a high surface area of the hilt. Many Qui-Gon Jinn style lightsabers, like Ultrasabers Consular or Saberforge Guardian, use a similar style shroud overlay as well.
The custom saber company Kyberlight [affiliate link] (first hilt on the left) does something interesting with shrouds. Kyberlight uses a removable shroud or sleeve that fits over the body of the hilt. I have a black shroud installed, but I can easily remove it and exchange it with a different one. Kyberlight currently offers 13 different sleeve accessories (shrouds) for its hilt. I don’t know if any other custom saber companies use removable shrouds, like Kyberlight, but it’s a neat concept.
Lightsaber emitter shrouds are a common design feature. The black slanted emitter shroud on the Darth Vader lightsaber (third hilt from the right) is one of the more famous examples of an emitter shroud. The Jawa’s Junkyard Gungi lightsaber (first hilt on the right) incorporates a larger emitter shroud into the design as well.
Sometimes a lightsaber enthusiast will add a custom shroud to the lightsaber hilt or commission a sabersmith to add a shroud to the hilt. Adding a shroud can be a fun way to customize or mod an otherwise relatively basic or simple hilt. Some lightsaber enthusiasts will add a shroud to a basic Ultrasabers lightsaber, for example (e.g. Apprentice, Initiate, Aeon, Sentinel, etc.).
A custom shroud could be made from metal, PVC, or other materials. The shroud could be simple in design or ornately acid etched, weathered, powder coated, etc.