I know there are three types -
desktop external HDD - needs to plug in for power, so it isn't very portable and mainly stays in one place
portable external HDD - gets its power from the USB ports on the computer it is plugged into, might need to plug into two USB ports at once
NAS Wifi Server type - lets everyone in the house connect to it for storage and access to shared files like music and images. The good ones aren't cheap, and the cheap ones aren't good. (So I've heard.)
Talk to me.