I think that they are for recording the moves on the computer, electronically.
What are these cords?

Those are DGT boards. They can be plugged into a computer to play against software, on the internet, or just record moves. It looks like Kasparov was playing Deep Junior.
http://digitalgametechnology.com/site/index.php

I just scoured their web site and found this:
"Modern, reliable, sensor technology recognizes each piece accurately and fast.
Each piece is identified by color and type. This gives you extra reliabilty in fast blitz games and makes setting up chess positions very easy."
It seems they can distinguish between the men but I didn't find anything about how they do it.
I've seen these things in other pictures to, the cords coming out of the board. What are they for? Here's the link in case the picture doesn't show up. (it's not for me)
http://woodytondorf.files.wordpress.com/2009/06/ap_kasparov2_day2_f.jpg?w=468&h=336