As already mentioned by others, AHCI allows you to "hot swap" internal drives. You can't remove the drive containing a running Windows installation though, because it is constantly in use and therefore can't be unmounted.
I had the same problem too. My SATA6 "C" drive was being shown as being removable. After doing a lot of Googling I found none of the suggestions worked. My system is a
Z77X-D3H Gigabyte MB with a WDC 1002FAEX as my system drive. What I did to fix the problem was go to "Device Manager-Storage Controllers-Marvell 91xx-Policies" and uncheck the box that says "Enable safely remove disks." Problem solved, for me.