<operating system> (FS, or "filesystem") 1. A system for organizing directories and files, generally in terms of how it is implemented in the disk operating system. E.g., "The Macintosh file system is just dandy as long as you don't have to interface it with any other file systems".
2. The collection of files and directories stored on a given drive (floppy drive, hard drive, disk partition, logical drive, RAM drive, etc.). E.g., "mount attaches a named file system to the file system hierarchy at the pathname location directory [...]" -- Unix manual page for "mount(8)".
As an extension of this sense, "file system" is sometimes used to refer to the representatation of the file system's organisation (e.g. its file allocation table) as opposed the actual content of the files in the file system.
Unix manual page: fs(5), mount(8).