Active directory is esentially a way of organizing users, groups, shared resources, and security settings for retrieval by the operating system when authenticating users.
Trees are collections of domains sharing a single namespace and forests are groups of trees.
If you want to share a files on a network you need to create a share, if the resources you want to share actually consist of files scattered on a bunch of different machines, you would have to create shares on each of them. This is an especially good deal for networks for larger companies or organizations where the multiplicity of places that store data could overwhelm the user trying to access it. So users would not have to worry about losing their connection to the files they need.