It’s rather simple actually….humans (and many animals) have what’s called stereoscopic vision. This means our brain is able to take input from two sources (our eyes) and turn it into one single 3D image – giving us depth perception.
Videos like the ones you linked (the first link is broken btw) use two images that are *slightly* different. The image on the right is as if it were seen from a left eye, the image on the left is as if it were seen from a right eye. When you cross your eyes so the images align, our brain is able to take the input from each side as if our eyes were actually seeing that area in real time – a slightly different point of view from each eye. So, as it does really well, it merges the two different images into a single 3D image.
tl;dr – Your brain is really good at merging two slightly different points of view (one from each eye) into a single 3D image, videos like you posted are designed to allow your brain to do this when you cross your eyes to align both images.
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