What is EIFS? This is a question that is easy to answer, but difficult to show. Adex Systems (a manufacturer out of Montreal) has put together a FANTASTIC video showing what the basics of the EIFS system. The visual aspect of the video makes it much clearer what constitutes the various layers and what they look like.

Here is the video: http://www.adexsystems.com/video/Adexres-rs-en.htm.
And here is the overview and specifications for the system: http://documentation.adexsystems.com/index.php/eng/content/view/full/1271.

Note that most large manufacturers have an identical system using similar materials. Adex has just done the best job of clearly laying it out.