To mount is to attach or otherwise make accessible or available something to the computer it’s mounted on.
The term originates back in the days of mainframes using large disk-packs and reel-to-reel computer tapes. When the information on one of the packs or tape was required, the computer would display a request for the computer operator to actually locate and physically mount the the pack or tape in its respective disk or tape drive. Once mounted, the data stored on these devices could be accessed by the computer.
Today the term has less of a physical connotation and more of a logical one, but the fundamental concept remains the same.
Instead of a physical disk or tape, files such as ISO files, TrueCrypt volumes, or even some backup images can be mounted using the appropriate software, making their contents appear as an additional virtual disk drive on the computer – perhaps drive “Q:”, as an example. Once mounted, the contents of these files can be read and written by simply accessing the newly added virtual drive that appears when mounted.
Unmounting, or less commonly, dismounting, is the reverse: taking the file that has been mounted and detaching it from the system, so its contents are no longer accessible via a virtual drive.