Cover one eye and look at something, then uncover the eye, and notice the added "depth" information. Personally, I don't observe the depth information from stereo vision in a way that I can easily describe in terms of a (single) photographic image.
Apparently the images from the two separate eyes are combined after processing some of the depth information. My consciousness does not seem to have direct access to the entire pipeline.
(I made some goggles to experiment for longer durations. Great fun.)
Similar things apply to face recognition, instantly comprehending words from letters, mathematical formulas (possibly only for trained mathematicians), and perhaps even fear of spidery images.