I've never personally used
manifests, which are a relatively advanced Hammer feature. From what I understand, it's basically a method of splitting your map up across multiple files, which are viewed and edited from within one "master" file and can be "toggled" on and off as needed. If you've ever used an image editor that has layers, like GIMP or Photoshop, it seems to be a lot like that. It's also a technically unfinished feature; there's a bit of extra setup required to properly compile a map using manifests, which is probably the main drawback. Outside of version control, it's an
arguably redundant feature, as there are plenty of other ways to manage what is or is not visible in your map (
quickhide and
visgroups, the latter of which is fairly functionally similar to manifests, although not quite as fancy). Regardless, some mappers do swear by manifests, and so it might be something worth checking out once you get the hang of the rest of Hammer's tools and are looking for ways to optimize your workflow.
If you're really interested in trying out manifests, I'd advise getting started with
this guide.
EDIT: Also, manifests in Hammer should not be confused with
particle manifest files, which are a totally unrelated thing.