3D vision is enabled by the ability to discern which objects in the field of view are close and which ones are further away. 3D vision is possible because we have two eyes. The two eyes are a few inches apart, and therefore view the world from different perspectives. The closer an object is to you, the bigger the difference between the images perceived by your two eyes. The brain is therefore able to infer how close something is by considering the difference between the viewpoints of your two eyes. The bigger the difference between the two images, the closer an object is.
If you hold a thumb in front of your face and view it with only one eye and then with the other, the thumb will appear to be changing positions. The closer the thumb is held to your face, the more it will appear to be changing positions when you switch from one eye to the other.
This is also why judging distances is difficult or impossible if you cover one of your eyes. If you cover one of your eyes, you are no longer able to see things in 3D, because your brain is only receiving one viewpoint and is not able to compare it with a different viewpoint. It therefore cannot calculate how far away the object is.
3D movies exploit this effect by superimposing two staggered images on the movie screen. The difference between the two images is made large for objects that are supposed to be “close” and progressively smaller for objects that are supposed to be further away.
But that is not enough: the key is to make each eye see only one of the images. This is where the 3D glasses come in. As mentioned above, two images are projected on the screen. One of them is polarized in one plane and the other is polarized in another plane. The glasses have two polarizing filters that have different orientations. The result is that one filter on the glasses only lets one of the images on the screen through it, while the other only lets the other image on the screen. In this way, each eye sees something different, which is exactly what we need for 3D vision.
This is why if you take your glasses off, you will see that two different images are being projected onto the screen. The effect is of course particularly obvious for objects that are supposed to be “close”, because the difference between the images is greater for them.
Note that the polarization of the images has absolutely nothing to do with the 3-D effect. It is simply a very effective technique by which each eye is allowed to see only one of the two images, to the exclusion of the other. The 3D effect is created by the fact that the two eyes are looking at two different images, with the difference between the two images being greater for objects that are close. For a given element on the screen, the bigger the difference between the two versions of its images, the more it appears to stick out from the screen.
It is, of course, nothing more than an illusion that exploits the way the brain works.
When you put your glasses on, the disconcerting “double vision” goes away, and what you see instead is an absolutely convincing 3D image. The brain is fooled into thinking that it is looking at a real scene (as opposed to a flat image projected on the screen) because it is receiving different viewpoints from each eye, just as it would if you were looking at the real world. When the difference is large, it interprets it as “close,” if the difference is smaller the object will look “further away”, and so on. Amazingly, we now also have 3D televisions!
Disney loves to make its logo protrude far away from the screen, very much in your face. If you take your glasses off, you will notice that there are in fact two logos that are very staggered. If you look at something that is “in the distance,” you will see that it is not staggered anywhere near as much. An object that is at infinity will have its two images exactly superimposed (not staggered), because if something is at infinity the two eyes have exactly identical views of it. This is why if you look at an object that is very distant, looking at it with only one eye and then with the other will not produce the position-shifting effect that you see when you hold your thumb in front of your face.