A file manager, also called file browser, is a software or App, which provides functionalities to manager directories and folders on a file system. These functions mostly, but not always and not exclusively, include to delete, copy, move create or modify a file.
View of files and folders
The basic feature of a file manager is the ability to show directories and the content of these directories, which mostly can be some more directories and/or files, as well as navigating through the structure of these directories. The functionalities differs between the different available file managers. E.g. some managers are able to view hidden fiiles (like shown in the right image, hidden folders are transparent), others managers may show the file structure more intuitively.
Show meta data
Like in the Windows Explorer (the file manager of the Windows operating system), a lot of file managers for Android have the ability to view the meta data of a file or directory, like the file size, storage location or creation date.
Rename and create
Most file managers provide the possibility to select a file to edit it, however, a separate app, which supports editing the file format, is needed to actually edit the file. Most file managers, on the other side, provide renaming files out of the box, as well as creating a new file or directory.
Move, copy and delete
Another basic functionality of most file managers is the management of files like move or copy. When moving a file or directory, it will be moved or copied from the original destination directory to a new one.
A root-explorer is needed to edit protected files and directories, like files and directories on the /system partition. A root explorer executes the commands (move, copy, delet, ...) with root permissions against the file system. However, the device needs to be rootedto allow these actions, as well as a file manager, which allows to run commands as root.
Some file manager apps provide, beside the management of local files and folders, a way to interact with foreign/remote systems, e.g. using a connection to a FTP server or samba share.
Well-known file managers
Some well-known file manager apps can be found in the Google Play Store: