What do we mean by mounting a filesystem?
Solution 1:
Way back in the dawn of computing history, storage consisted of paper and then magnetic tape. To connect storage to the computer you would literally hang or mount the tape on the tape reader. I'm sure that, for awhile anyway, after magnetic disks were introduced tapes hung around as file storage -- not merely back up. It was probably easier to reuse the existing terminology (and code) than invent a new concept for disks and thus we continue to mount a disk-based (or even network-based) file system.
Mounting a filesystem, means taking that storage and connecting it to the operating system in a way that it's usable as a hierarchical storage device with directories and files. This could be the initial filesystem (root of the directory hierarchy) or another filesystem that connects to the root filesystem at a mount point, extending the directory hierarchy. In that sense, it is like extending a tree by adding another tree to it.
Solution 2:
At the most abstract level, it involves adding the filesystem's information into the VFS such that file accesses are directed to the appropriate place on the filesystem.