MOst of them are powered off a floppy drive or 4-pin molex power connector. Data is usally supplied via USB or Serial, although I have seen Parallel ones.
The most commonly supplied manufacturers are Matrix Orbital and CrystalFontz although Silverstone and Thermaltake also do consumer displays and Ahanix make one specifically for HTPCs.
The cheaper ones only do characters, the more expensive ones have pixel addressable graphics. The ultimate extension of this principal is the Thermaltake LCD for the Mozart case which is basically a 7" in-car display and can display anything your graphics card can throw at it.
Some have buttons on that can be used for volume control and others have built-in remore controller functions that make building a fully-integrated HTPC easier.
The big benefit is if you want to use your PC without the screen turned on eg. as a video recorder or you need to display status without disturbing the main screen image, or you want to be able to turn up the volume or change channel without using the mouse or keyboard. I realise it's unlikely most people would want to do that, but it is possible with these devices.
In general they are just 'bling' for PCs.