A filesystem is the methods and data structures that an operating uses to keep track of files on a disk or partition that is, the way the files are organized on the disk. The word is also used to refer to a partition or disk that is used to store the files or the type of the filesystem. Thus, one might say ``I have two filesystems'' meaning one has two partitions on which one stores files, or that one is using the ``extended filesystem'', meaning the type of the filesystem.
The difference between a disk or partition and the filesystem it contains is important. A few programs--including, reasonably enough, programs that create filesystems--operate directly on the raw sectors of a disk or partition; if there is an existing file system there it will be destroyed or seriously corrupted. Most programs operate on a filesystem, and therefore won't work on a partition that doesn't contain one (or that contains one of the wrong type).
Before a partition or disk can be used as a filesystem, it needs to be initialized, and the bookkeeping data structures need to be written to the disk. This process is called making a filesystem.
Most UNIX filesystem types have a similar general structure, although the exact details vary quite a bit. The central concepts are superblock, inode, data block, directory block, and indirection block. The superblock contains information about the filesystem as a whole, such as its size (the exact information here depends on the filesystem). An inode contains all information about a file, excepts its name. The name is stored in the directory, together with the number of the inode. A directory entry consists of a filename and the number of the inode which represents the file. The inode contains the numbers of several data blocks, which are used to store the data in the file. There is space only for a few data block numbers in the inode, however, and if more are needed, more space for pointers to the data blocks is allocated dynamically. These dynamically allocated blocks are indirect blocks; the name indicates that in order to find the data block, one has to find its number in the indirect block first.
UNIX filesystems usually allow one to create a hole in a file (this is done with lseek(2); check the manual page), which means that the filesystem just pretends that at a particular place in the file there is just zero bytes, but no actual disk sectors are reserved for that place in the file (this means that the file will use a bit less disk space). This happens especially often for small binaries, Linux shared libraries, some databases, and a few other special cases. (Holes are implemented by storing a special value as the address of the data block in the indirect block or inode. This special address means that no data block is allocated for that part of the file, ergo, there is a hole in the file.)
Holes are moderately useful. On the author's system, a simple measurement showed a potential for about 4 MB of savings through holes of about 200 MB total used disk space. That system, however, contains relatively few programs and no database files. The measurement tool is described in appendix B.