Your eyes perceive depth by comparing the difference between the two "pictures" your eye takes. 3-d glasses replicate this by tricking your eyes into each seeing a different image projected onto the same screen

The old red/blue ones used red and blue light to replicate this (red light only went through the red lens, blue through the blue one).

Nowadays the RealD glasses (the clear ones) make use of light polarization, which is the direction the wave of light wobbles as it travels (like a sine wave from trigonometry class). One lens only lets light wobbling horizontally pass through, the other only lets the vertically wobbling light pass through.

Fun tricks with those RealD glasses next time you have a couple pairs: 1. Take a look at your friend wearing one and close one eye, one of their lenses should turn black and 2. Keeping one eye closed and looking at your friend wearing a pair, tilt your head and you should see the lenses change

To fix the edit: it looks distorted without the glasses because both eyes are seeing both images since our eyes can't detect polarization