My first gilded comment - thank you :)
I'm glad it actually helped - I was afraid that it was all a bit abstract, and I was explaining more the *how* it works than what it *feels* like (which is quite difficult to convey).
I was thinking of another comparison (which I didn't put in the first comment, because it was already getting long): The way depth perception *feels* to me is a bit like the effect of
$1 in computer graphics. AO is basically an advanced lighting/shading method in 3D rendering that also takes into account that objects can shadow themselves, depending on their shape. So it's not just "directional light hits object, casts shadow on another object".
If you look at the very first image in that post, you'll notice that there is no actual directional light source casting any shadows (that image consists *only* of an AO layer). All the shadows that are in there are the effect of that soft, diffuse ambient light not quite getting into all the nooks and crannies. Such an AO layer then would get combined with regular lighting,
$1.
Unless seen on its own, in a greyscale clay render like that, it's also quite a subtle effect. But it really accentuates the shape and plasticity of objects. That first image with the AO-only layer is like pure shape-ness, if you will. It puts emphasis on the edges of things, and helps separate them from their background.
So that's sort of what depth perception feels like to me. At least that's the closest visual approximation I can think of, that can be shown with 2D images. Unlike the picture of the sunflower field in your biology book :) I still don't quite understand how that could possibly work as an explantion.