Explain "buying debt"

[CrazyAce]

I read this paragraph:

"Just about everybody thought Lampert was crazy in 2002 when he began buying up Kmart debt at around 40 cents on the dollar after the retailer filed for Chapter 11. Crazier still, Lampert loaded up more as the price sank to 20 cents, eventually boosting his total investment to $700 million."

And I simply do not understand what "buying debt" means, at least in this context.

I've Googled 7 ways to Sunday and can't find an explanation.

Can someone give me a rundown of "buying debt," and, if you're so kind, apply it to the article segment I quoted.

Thanks guys