Mounting a volume means putting it somewhere in the file system so that it's data becomes available. For example, mounting a flash volume named
MyFlash usually creates to a folder named
/media/MyFlash from which it's contents can be accessed.
Unmounting it means making it's data unavailable through the file system. That means either:
/media/MyFlash does not exist any more after unmounting, or
/media/MyFlash is an empty folder
Also you unmount one partition at a time. If you have multiple volumes (partitions) on your drive, you need to unmount each one separately.
a drive means the kernel USB module does not care about the drive any more. Any outstanding data that will be written, the device will be powered down (though there will still be voltage going out of the USB port). Only after this has finished should you remove the drive from the USB port.
Even if the kernel writes all it's data through the USB port, some devices, especially external (rotating) hard drives, may buffer this data and not write it to the disk immediately. Just unmounting all partitions and pulling away the USB cable may leave data in these buffers unwritten to disk and thus lost. However, when safely removing the drive the kernel tells the drive to make sure all data is written and waits until the drive confirms to have done so.
The kernel associates some special files with devices. Say we have a device
/dev/sdc with two partitions
/dev/sdc1. Mounting and unmounting operations make use of these files and formatting tools use them to write data directly to the partition. But when you "safely remove" the drive the kernel no longer associates any
/dev/sdc* file with your drive.
As long as the drive is not "safely removed", but just "unmounted" there is still a way for applications and the kernel to write to the disk, and there is no guarantee that the kernel has finished writing it's buffers to disk, or that the disk has finished recoding them.