Much like movement, our brains are designed to perceive depth; that is, we seem programmed with an innate ability to see in three dimensions.
This is especially effective on the Internet and in print, as a web page (or a magazine page) is two-dimensional. Adding a perceived third dimension to a web page can greatly enhance its power to catch your visitors' attention.
Note
A good example of the human brain being able to perceive 3D is Ames' Window, available through Professor Richard Gregory's website, at: http://www.richardgregory.org/experiments/video/ames_window.htm.
A more recent and web-related depth example is the website for Silverback (http://www.silverbackapp.com):
Interestingly, the vines are layered (using the z-index property in CSS and transparent PNGs) to give the viewer a notion of depth. The closer the vines are meant to be, the more blurred they are.