It probably gets more complex than this, but mapping a drive is kind of like creating a shortcut to drives, folders, files.
That way, instead of going through the entire network to save something or pull something down, you just use the "mapped drive" you made.
i.e. on ComputerA you want to map the C:Drive of ComputerB. You would map B's C:Drive, and call it whatever - X:, Y:, Z:, etc.
Like I said, it probably gets more complex, but that's a simple way of explaining it.