If you want to see a 3D image in a 2D plane (on your HDTV), you need a way to show your eyes slightly different images--that's how you "trick" your brain into perceiving depth. The easiest way to do this is to wear glasses that can help to present a different image to each eye. (Smaller displays, such as the one found on the Nintendo 3DS, don't need glasses because the display itself is designed to show each eye a slightly different image, but this technology doesn't work well enough for larger displays quite yet.)
Active-shutter glasses are actually small LCD screens that alternately dim the left and right "lenses" in succession. They rely on an infrared signal emitter in the TV that tells each pair of glasses when they should dim each lens, so each eye can see the image intended for it. Since active-shutter glasses are fairly complicated electronics, they're pricey: A typical pair usually runs about $150, and works only on 3D TVs made by the same manufacturer. They depend on batteries to keep running, too. What's more, they're kind of heavy--especially if you're already wearing prescription eyeglasses--which can make watching a whole movie somewhat uncomfortable.
