Let me try to explain:
There are currently two different types of 3D in mainstream use, the traditional Cyan/Red and the new Real3D stuff at the cinema.
Both work on the same principal. Your eyes both see different images, which are then merged by your brain to create an image with depth.
In 3D cinema/tv/still pictures the idea is to take an image of a scene at positions that are similar to the eyes, so there are two cameras seperated by a couple of inches (this can vary, but for now it will do). This will record images that are more or less the same as your left eye and your right eye.
That is all that is required extra at the recording stage.
The trick than comes at the display stage. The idea is to show only the left image to your left eye and the right image to your right eye. In the classic cyan/red images this was done with colour. By making one image entirely cyan within the image and one image entirely red, and then placing a red filter in front of the relevant eye and cyan in the other you can ensure that the left eye only sees the left image and visa versa.
To replicate this on TV requires no extra purchases, other than a pair of Cyan/Red glasses, they used this with the DVD of Journey To The Centre Of The Earth.
The main problem with this method is that you cannot have an image that contains any blue, green or red otherwise it will appear to the wrong eye and throw off the 3D, so most images are very dull.
The new method gets around this by using light polorisation. If you don't know what that is, it basically means that as light travels the waves are moving in a plane. Imagine light being giant flat plains of light, almost like pieces of paper. You can manipulate light and make sure that it moves horizontally or vertically, and that is the basis for the newer technology. The left image is filtered so that the light moves in one direction and the right image the other direction. The glasses you wear are then effectively filters that only either allow horizontal or vertical, so that again your eyes only see the correct image. Because any colour of light can be manipulated to travel in a direction it means that full colour images can be shown in 3D.
Taking it back to why you need a new TV, your current TV is not capable of producing light that is polorised in a certain direction. The new TVs will do that. The other option is that you can get special glasses that have shutters in front of each eye that open and close in time with the image on the TV so that it syncs up, but this isn't compatible with any but the most expensive LCDs/Plasmas.
There is no way currently that all of this can be done without glasses on a large TV scale. If anybody saw a recent Top Gear where they had a sat nav screen in the car that showed as Sat Nav to the driver and a DVD player to the passenger, this technology could be used to show different images to each eye without glasses, but would only work up to about a 10" screen and your position would need to be dead center.
I hope that explains it all!