A collection of files that can be accessed by name and are typically stored on hard disc. Files are chunks of bytes which can be read, written and appended, but typically not inserted.
CP/M, DOS 1.x, and the original AppleMacintosh didn't have HierarchicalFileSystems.
The MainFrame operating system VM/CMS had a non-hierarchical file system. That, plus the rather low limits on filename length, made working with it rather ... interesting.
These are nowadays (2005) considered anachronistic and not-quite file systems. That's probably the reason why FileSharing systems aren't called file systems. But historically they are and the modern ones are just hierarchical cousins.
See also FileSystemAlternativesCategoryFileSystem