Some of them translate trivially to photos/TV/etc, like convergent lines or texture gradient. Some of them are surprisingly physical, like feedback from your eyes about vergence or focal distance.
Stereo is highly effective up close, say within 10 meters (yards). And it works faster than many modes. It's absolutely fantastic for catching things out of the air. Given our intraocular distance, it's basically garbage past, I dunno, 30m or something? (obviously it degrades smoothly across distance)
I've heard more than one academic (evolutionary cognitive psychologists, etc) speculate that the single biggest evolutionary advantage of having two eyes is to have a spare in the event of damage. That might well be just whimsy and exaggeration, but I think it puts a helpful alternate perspective on it (pun!).