Its not going to. The graphics card limits to 60Hz on DVI, HDMI and Display port. (85Hz on VGA).
120Hz and 240Hz TVs will only display video in those refresh rates when post-processing is turned on. The additional frames are inserted by a "frame interpolation" engine inside the TV. When you connect a PC or game console to a TV it will either detect that fact and turn the post-processing engine off or you will have to turn it off manually (this is probably why your TV is only reporting 60Hz as an available refresh rate for your PC input). If you don't it will make games difficult to play because the post-processing engine causes a delay between the input and the display (it takes time for the post-processor to process the video stream, so there's output lag). In the case of 3-D TVs the higher refresh rate makes sense, because every frame needs to be displayed twice...once for each eyeball.
There are 120Hz monitors, but the higher refresh doesn't do much good unless you can actually v-sync the video output to the monitor to 120fps. That means you need a minimum of 120fps (not average) to avoid frame tearing. I'm guessing that a very small percentage of people have the CPU/GPU combinations that are able to do that with many modern games. I'm guessing that there just aren't enough people clamoring for it to make it worth the effort of supporting it at the moment.
