Allow me to break it down for you.
First you need to understand the very basics of 3D and how we (humans) see in 3D. This is accomplished by our two eyes, at a set distance apart, working together. We see an image from 2 slightly different viewpoints at the same time. Our brain puts the two images together and determines depth based on how far or close those same two images are from each other. We do this automatically, and we do it on a per object basis. So if you put your hand real close to your face, you'll see two of the same object (your hand), and it will be out of focus. If you pull your hand back slowly, as you focus on it you will see the two images merge into one object.
So to "trick" our brains into seeing a 2D screen as being full of 3D objects, the screen needs to somehow direct specific images at specific eyes. So you will have an image that only your left eye sees, and an image only your right eye sees. If these two images appear so fast (90 times per second or more) that we cannot tell that its two images, our brain puts it together as one image. And there you go, its just like seeing 3D in real life!
There's a few ways of getting images to only show to a specific eye. The method you see in theaters is called "polarized". To make it simple, this works by putting a filter on the projector that rotates or flips to make the light travel either horizontal or vertical once reflected off a screen. The glasses you wear in these movies have one eye that can only see horizontal light, and one eye that can only see vertical light. This is a REALLY simplified explaination. The issue with this system is you actually lose a lot of light that's being reflected back at you, because half of it is being lost in the glasses. The other problem is the mechanical motion of "flipping" the filter can cause crosstalk (when you see both images at once). The biggest reason that this isn't used in the home is because the screens that have these filters on them are usually 8 to 12 times more expensive than a normal HDTV. But the glasses are really cheap (~$1).
The method being used at home is very different. It uses a cheap screen (by comparison, at least) and expensive glasses. The HDTV only has to be able to display 120Hz, which means the TV can change the image on the screen 120 times per second. This breaks down to 60 frames per second per eye. So it shows the left eye, then the right eye in full frame, but it happens so fast it appears as one single (blurry) image. The glasses are actually are very small electronic screens themselves (LCD) that can turn clear, then totally black very fast. So it syncs to the screen so that when the left frame is shown on the screen, the right eye lens goes black. That way you only see the left frame with your left eye. Then the same happens to the right eye. This happens 120 times per second, and thus you see 3D as you would in real life. And because this is a digital process, you get less crosstalk than with polarized. But crosstalk is still present.
So there you go. I know this post is REALLY long, but its the easiest way to explain 3D in its current format. Don't even get me started on explaining autostereoscopic (3D without glasses). I don't even think I fully understand that tech yet.
And for all the 3D savvy folks reading this, please excuse the info that isn't 100% correct. I was just trying to make it easier to understand.