If you're planning to hook up your computer to your TV and drive it at 120 Hz, in all likelihood that's not going to work.
120 Hz TVs exist for one reason. Movies are shot at 24 fps. If you try to display that on a 60 Hz TV, you end up having to show one movie frame for 3 TV frames, the next movie frame for 2 TV frames, the next for 3 frames, the next for 2 frames, etc. This 3-2-3-2-etc timing causes an uneven jumping effect called judder. Smooth panning shots and motion look like they're jumping and stuttering.
The only solution on 60 Hz TVs is to interpolate frames and produce 60 fps, 36 of which are made up via interpolation. This produces the dreaded soap opera effect, where the movie looks like video because it's now 60 fps.
The alternate solution is to increase the TV's internal refresh rate to 120 Hz. Then each frame of your 24 fps movie can be shown for 5 TV frames. There's no judder, and smooth pans and motion remain smooth. Unfortunately, this is almost always an internal function of the panel, and not something you can access via the HDMI or DVI inputs. Those are still limited to 60 Hz. (Movies on DVD and blu-ray are transmitted to the TV at 24 fps, so the TV's internal processing knows to display them at 120 Hz.) Likewise, if you don't care if movies are shown in their native 24 fps or interpolated to 60 fps, then you don't need a 120 Hz TV.
240 Hz TVs are the exact same thing, except for 3D. The left and right images are each shot at 24 fps, so the TV needs to display 48 fps total to achieve the 3D effect. 48 doesn't divide into 120 evenly, so they have to bump up the refresh rate to 240 Hz.
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