You know the drives you have in Windows? Like C:/ and D:/ and stuff. One of them is just your hard drive, and one of them is your cd drive, and if you plug in a flash drive or external hard drive, that'll make another letter appear. Your shared folder is the same; it's not your computer's hard drive, it's some other drive, somewhere else.
Now, that flash drive, and your shared folder, and all of these--they're not on your computer the second you plug them in, or connect remotely, or whatever. They're not in your "file system". They have to get thrown into the mix, and your computer has to read them, and know that they're there, and give you a way to access them. This is "mounting"--plopping the drive into your file system, where you can get to it.
In Windows, when a drive is mounted, Windows will pick another letter, and assign that letter to the drive--and then you can access it from "My Computer". On Unix like systems such as Ubuntu, They go with the much nicer system of placing that icon on your desktop. So when you plug in your flash drive, instead of getting some stupid autorun dialog that is totally annoying and sometimes unsafe, you get a nice icon on your desktop to symbolize the piece of hardware you just stuck into your computer.