According to Wikipedia the Droste Effect is any image which contains a smaller version of itself somewhere in the image. Lately it seems that any image produced with "the Droste code" can be called a Droste image.
"The Droste code" is the code written and released by Josh Sommers to the discussion forum for the "Eschers Drost Print Gallery" flickr group. The code is a script for Mathmap, which is itself a plug-in for GIMP. The code allows you to do all sorts of interesting recursive patterns.
The code is based around some mathematics that were found to be able to mimic the distortion seen in MC Escher's "Print Gallery."
Here is one of my favorite Droste images. It combines all of the photographic manipulation techniques that I have in my tool kit at this point. HDR, spherical panorama, stereographic projection, and Droste effect. Whew!