They are cables that connect your hard-drives and cd/dvd drives to your motherboard (or adapter).
"Standard" ones are flat-ribboned, rounded ones take the 40 cables and sheath them in some sleeving so that the cable is now round rather than flat.
Round cables reduce the airflow restriction in your case which is good for many reasons...

(haha beaten by Mangar by a minute!)
Cool, ok, may as well post something extra:
so you've got 40 pins on the connector, but you can also get 80-conductor ATA cables that are supposed to be better for high-speed ATA hard-drives...
haven't actually tested the difference but I've got 2 Akasa rounded ATA cables that are 80-conductor... and they also light up!

You can also do a home-made version with your existing flat-ribbon ATA cables (I had to do this for the SoundBlaster LiveDrive cable that connects my soundcard to the front-panel-drive-bay-audio thing)
Take the cable and hold it in both hands, index fingers and thumbs about 4 or 5 wires along, and kind of pull them apart like you're tearing strips of paper or something. Do this every 4 or 5 along (or every 1 or 2 if you can be bothered!) and then you can either get a bunch of elastic bands and space them out along the cable (you know, pull them tight twist and pull over again etc around the wires) or use electric tape...

+ Free

- Takes a bit of time