1. Debugging statements inserted into a program that emit output or log indicators of the program's state to a file so you can see where it dies or pin down the cause of surprising behavior. The term is probably a reference to the Hansel and Gretel story from the Brothers Grimm or the older French folktale of Thumbelina; in several variants of these, a character leaves a trail of bread crumbs so as not to get lost in the woods.
2. In user-interface design, any feature that allows some tracking of where you've been, like coloring visited links purple rather than blue in Netscape (also called footprinting).