I read that one way to avoid identity theft is to avoid using digital photocopiers. What is digital, and how would using a digital photocopier be dangerous to one's security?

An analog photocopier basically reflects bright light off of the original document onto a "drum" which is charged. Anywhere that the light hits the drum (the white areas of the original), the charge is removed. Then a powdered ink (toner) is put on the drum, and it sticks to the areas that are still charged (dark areas on the original). Then paper is put on the drum, and the toner is transfered to the paper. The only place that there is an intermediate image is on the drum, and this image is destroyed after every copy (you can't copy something else without making a new image on this same surface).

Digital copiers are basically a scanner attached to a printer. The scanner makes an electronic picture of the original and stores it in its memory, then prints the picture. Some digital scanners can save the intermediate image. The idea is that this lets you make multiple copies of multi-page documents. Each page is scanned once and stored in the copier's memory, then they're printed in order (collated). I've never thought about this as a security risk, but I guess it would be possible that someone could get at these saved images.

It sounds as though we should not be using our own computers' printers, which scan, to copy documents containing sensitive information (information better kept confidential).