Glossary
FAL (File Abstraction Layer)
The file handling of TYPO3: every file is a record with metadata, not just a path in a directory.
A file is not a path
Without an abstraction layer, an image on a website would only be a path in a template. Where else that image is used, whether it has an alternative text, and who uploaded it: nobody would know.
FAL turns it into a record. Every file gets metadata and an identifier; references point at that identifier rather than at a path. A file can therefore be moved without breaking references, and alternative texts are maintained once instead of afresh at every use.
Storages
An installation can have several storages. The normal case is a directory on the same server, but remote storage is equally possible. The application notices nothing, because it works with identifiers rather than paths anyway.
For editorial teams it is mainly a permissions question: storages can be assigned to user groups, so a department only sees its own area.
Where it gets stuck in practice
Two things come up again and again. First, collections that have grown without order, in which the same file sits several times over. That can be tidied up, but only with an eye on the references. Second, missing alternative texts: they belong to the file rather than to the individual use, which makes them an accessibility matter for the whole site.