The Deep Web consists of all information on the World Wide Web which cannot be located by general-purpose search engines (Google, Yahoo, Bing etc.). There's a large amount of information which even powerful engines such as these cannot find.
Sometimes you'll hear the term "Dark Web." These terms are sometimes used interchangeably, but the deep web and the dark web are not the same thing, as this helpful article from BrightPlanet explains: Clearing up Confusion: Deep Web vs. Dark Web
There is nothing inherently special about Deep Web pages. The Deep Web is largely the product of limitations in web crawler technology. As technology changes, so does the Deep Web.