You know how when you cross your eyes you get like two different perspectives of whatever you're looking at? Well if you focus in the right way, there's a "middle" perspective between those two. That is where I can see these stereograms or whatnot.
What you're describing is the cross-eyed way. The parallel way has the disadvantage that the separation between the two images can't be too big (no more than about 5 cm at arms length is my guess), while cross-eyed images can have very large separation (e.g. two side-by-side images[2]).
In return, once you learn how to put your eyes into parallel mode, it's incredibly easy and quick to do so compared to cross-eyed viewing, and much much less taxing on your eyes (since they are pointing in only slightly unnatural angles), and with more easily discernable details.
(also, if you try to view an image with the opposite viewing method it was designed for, it'll come out with the depth inversed, e.g. the raptor image linked by another poster[3] should stand out, rather than look "punched-in")
[1]: http://www.vision3d.com/3views.html
[2]: http://farm3.staticflickr.com/2073/1620326328_6dc93774bc_z.j...
Try it on this picture of a dinosaur[1], notice the 7 white bird-like shapes repeated across the page. Cross 2 of those over and you should see the image of the dinosaur appear.