Info about Mount and unmount SD card
Mounted: the card is integrated to your computer, phone or whatever and ready to use.
Unmounted:the card isn't integrated and can safely be removed, without causing damage.
As far as I understand it, "mounting" means the OS will read the SD card file system so it becomes aware of the contents and becomes in control of the reading and writing operations to it. "Unmounting" means the OS gives up control of the SD card so that other processes, like copying files to your PC and back can access the SD card.
I know it sounds a bit archaic for such a "modern" OS. Even my much maligned Windows Mobile phone I had before didn't require this mount/unmount business.
Maybe some of the more experienced Android/Linux members here can shed more light on this topic.