The workshop manual for my MG usually describes assembly as the reverse of disassembly and the reverse is more or less true for unmounting a file system.
A file system cannot be unmounted if something in the system is using one of its files. So, for example, you cannot umount /mnt/cdrom if a process is using that directory or any of its children. If anything is using the file system to be unmounted there may be VFS inodes from it in the VFS inode cache and the code checks for this by looking through the list of inodes looking for inodes owned by the device that this file system occupies. If the VFS superblock for the mounted file system is dirty, that is it has been modified, then it must be written back to the file system on disk. Once it has been written to disk, the memory occupied by the VFS superblock is returned to the kernel's free pool of memory. Finally the vfsmount data structure for this mount is unlinked from vfsmntlist and freed.