A file system is the specification of how files in a computer should be stored, named and organized. This tag should be used for generic file system questions. For specific file system questions (FAT, NTFS, ext4, ...) use the appropriate tag instead.
File Systems (or filesystems)
A file system is the specification of how files in a computer should be logically stored, named and organized. File systems present to users a human-readable format of data organization in the computer, where each file is a discreet unit of data.
File systems present only a logical format. They don't necessarily reflect the way the data is physically stored on a computer disk drive, or other storage device. Since the computer actually stores data in bits, data on a storage device lacks any structure; consisting of nothing more than a series of 1s and 0s.
File systems therefore give structure and meaning to that data, by — at the very minimum — giving an arbitrary collection of bits a file name and maintaining a record of this file physical location on the storage device.
Other than file names, common file systems also describe and maintain directories and file attributes, which serve as a means to further structure data organization and to give files specific purposes, security features or functionality.
File systems usually store this information in table-like format in a specific region of the storage device. Each file is listed on this table with its location, length and other properties clearly declared. An operating system that understands the filesystem format can then read this table to access a file in order to edit, rename, delete, move or alter any of its attributes.
For more reading
File System, at Wikipedia