What does it mean to mount something?
When you 'mount' something you are placing access to the file system contained within onto your root file system structure. Effectively giving the files a location. This is similar to the C:/D: drive labels in windows, but more flexible.
Mounting /dev/sdb1 to /mnt/disk1 places all the files and folders contained within the device standard disk B partition 1 into the directory /mnt/disk1 where you can access them.
Modern systems have ways to auto-mount drives just as windows auto-mounts drives to drive letters, but the location mounting system in Unix is much more flexible. And unmounting is obviously the removal of the access to those files/folders from that location. You can find out what file systems are mounted by running the command:
mount
Parts of ubuntu involved: mount, umount, fstab (for fixed mounts), udev, gvfs (for automatic mounting)
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.
A physical device can be either "unmounted" or "mounted". However, while the "unmounted" state for a physical device still appears on your desktop and still is under Places, a shared folder has a different behavior.
When you connect to a shared folder by using the "Connect to server" menu option, what Ubuntu does is it creates a sort of virtual folder. It's not actually mounted under "/media", but is using a special virtual network filesystem. In fact this is closer to mapping a network drive under Windows; they do not appear under your C:\ drive, but are instead given a different drive letter, which is basically just a convenient link to the folder. In Ubuntu, the listing under Places and the icon on your desktop is the same, just a convenient link. If you connect to the folder by going through Network, you're browsing straight to the folder, just like you can in Windows.