The origin of Chell's boots from Portal is explained in this Aperture Science video.
After offering us Aperture Science investment opportunities for panels, co-op robots, and turrets, Cave Johnson is back with a fourth that any Portal 2 fan should be familiar with: the Long Fall Boot. If you're going to be making your way through test chambers, it's a must have.
Managing velocity while having two "quantum space holes" at your disposal isn't the easiest task, but this "foot-based suit of armor" makes it so you don't have to worry about such things. You may have been wondering what main character Chell was wearing on her legs in Portal, and now you know.
The boots are "expensive as hell," but as part of the equipment necessary to stop a sentient AI from taking over the world, or whatever GLaDOS had/has planned, they're a worthy investment. The video also gives us a look at Chell when she was just an Aperture Science test subject, and she pretty much kicked ass back then too.
Chell, and her boots, will return on April 19 when Portal 2 is released for the PS3, Xbox 360, and PC. In the meantime, you might want to follow the content coming out of the Portal 2 ARG.