Active 3D Technology Using Active Shutter glasses
The following explanation might sound a little far fetched, but it really is how active 3D technology works...
The screen switches rapidly between showing the image intended for the left eye and the image intended for the right eye. It switches between images at least 100 times per second, more frequently on many 3D TVs.
But this wouldn't do anything useful without a way to ensure that the images intended for the left eye only reached the left eye, and the images intended for the right eye only reached the right eye... It's the active shutter glasses that accomplish this...
The lenses on these shutter glasses can turn from opaque to transparent and back again in an instant. Metaphorically speaking they're like shutters opening and closing. A wireless signal from an emitter on the TV tells them when to open and close, and they do it. In time with the alternating images on the TV itself...
So, when the TV is showing an image for the left eye, the left eye's shutter will be open and the right eye's shutter will be closed. A fraction of a second later the TV will refresh to show an image for the right eye, and the right eye's shutter will open and the left eye's shutter will close.
It sounds like a recipe for a headache, but it actually works very well. The "shutter" in "active shutter glasses" might suggest a clunky bit of plastic banging up and down. But actually the shutter glasses use liquid crystal technology, and the liquid crystals can be made transparent (open shutter) or opaque (closed shutter) efficiently and silently. And the shutter rate is fast enough for the system to work without visible flickering. Just like how there isn't visible flickering on a regular TV with images that refresh 50 or 100 times a second (50 Hz or 100 Hz). In fact, the refresh rate is limited more by the speed at which the TV can refresh than the speed at which the liquid crystal glasses can shutter open and closed.
Active 3D appears to be the mainstream option at the moment - most of the major manufacturers are making active solutions. Though in my opinion the shutter glasses bring some big drawbacks: they're expensive, bulky, and they require batteries or recharging to run.