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

to clarify my question: how is it that 3D movies look so distorted but when you use the glasses you can see it well. what do the glasses do exactly to make that happen?

This may not quite be eil5 level, but

You remember old 3d movies with the red and blue images? The way those worked is when you wear the red and blue lens would block one image per eye. So the red lens blocks the blue image, and the blue lens blocks the red image.

This in turn emulates how you actually see in 3d where each eye sees separate images.

Newer 3d movies work on the same principle, but instead of using colors to do it, it actually uses polarities of light. So when you look at the screen without the lenses it looks distorted and blurry because you're seeing 2 images. The glasses block one image per eye depending on the polarity. This allows you to still see all the colors too compared to the red and blue method.

Besides polarization (like mentioned in other answers) there is another technique (albeit it might not be as commonly used today): Active Shutter 3D system.

These glasses is, usually, a lot bigger, and needs batteries. They work by blocking one eye (like an eye patch), and then quickly switching to the other eye. The glasses do this really quickly. And at the same time the projector (or TV) shows one image for say the right eye, and then quickly changes to an image for the left eye. The TV/projector sends a signal to the glasses so the glasses switches eye at the same time as the TV/projector.

The difference between the two images is that one taken a little to the side to the other. Where the right image might show a little more of the right side of an object, and vice versa, this gives a perspective effect. And since this is how our eyes work, and how we perceive depth, you perceive the things on screen to have a depth to them.