There are a variety of different types of 3D but they all rely on the same basic premise.  If you’ve ever looked at something with one closed eye then opened it while closing the other and the thing you’re looking at moves slightly, it’s because of the distance between
our eyes.  This is how we’re able to perceive depth.  When we watch something on a screen we see the same flat image with both eyes so we perceive it as two-dimensional but if each eye is seeing something slightly different it gives a two-dimensional image the illusion of three dimensions.

Diagram of how we perceive depth

Anaglyphic 3D is one of the earliest technologies to create the effect through the use of different colors for the separate images.  One lens would have a blue tint and the other would be red and you’d look at a picture that combines two of the same image in the corresponding colors.  The eye with the blue lens focuses on the blue tinted image and the eye with the red lens focuses on the red image and since both images are set slightly apart at a precise distance, we perceive it as having depth.   This technology was first used in the early 1900’s and more recently played a big part in the theatrical release of Spy Kids 3D by Robert Rodriguez.  Much of the concept art for The Hobbit franchise was drawn using anaglyphic techniques as well since the film was going to feature lots of 3D effects.  However, this technique is no longer used for feature films because the red and blue drastically distort the color of the film.

Theaters now use a method of passive 3D where each projected image and lens is polarized in a slightly different way.  Without going into the science, what this polarization does is it prevents the light from one image from going into the lens of the other.  This ensures that each eye is seeing a slightly offset picture so that when we’re watching a film our brains combine what we see into a single perception that has depth.  That’s why when you take off the glasses the film appears to be blurry, because you’re looking at two projections of the same film that are slightly offset.

When looking through one lens the other appears to be black because of the polarization.

This type of passive 3D is the most expensive because it involves polarized lenses and projectors that need to be precisely distanced.  For most home televisions that boast 3D capability, they use a more affordable method called active 3D which creates a similar effect by rapidly darkening the lenses at precise intervals.

Whether or not you enjoy 3D movies the technology involved is quite advanced and uses some very fascinating techniques that trick our brains into perceiving flat images as three-dimensional.  It’s also a great way for theaters to bump up ticket prices a few dollars.  If you’re interested in learning more about how 3D technology works, Brady Haran produced an excellent video that explains more of the science involved.