Traditional television used (uses) an interlaced scan approach to drawing frames. So, on one pass the odd numbered lines of a frame will be displayed, followed by the even numbers of a frame. Under this approach a 60Hz television actually only displays 30 full frames (60 fields), but the human persistence of vision creates the illusion that you are seeing a full 60 frames and motion on the screen appears to be fluid. In reality you are seeing 60 fields per second, instead of full frames. This is true for NTSC televisions like we have in the U.S., but for most European countries and perhaps others too it is a 25/50 approach.
If your television indicates that it has a progressive scan mode, then you are seeing each line drawn progressively until the screen image is completed to fill the frame. Thus, 1080i is an interlaced scan device, while 1080p is progressive scan.
When you get into the 120/240Hz range what you are talking about is refresh rate of the display more than you are frame rates. The higher the range the more likelihood you are to reduce flicker and improve motion rendering. So, on a 120Hz television the entire image will be reconstructed and displayed 120 times each second. On a 240Hz system that is 240 times each second. Does this mean you are getting 240 FPS? No. While the television is refreshing the image 240 times each second the image may only change 24 times each second, or 25 times, or 30. . . it depends on the signal input. In fact, in some cases a 240Hz system may not even accept your input signal depending on how the system is set (a 1080p/60 will not take a 24fps input, for instance). However, there are systems that can take a 24fps signal and interpolate 1080p/60 (via pulldown), but it does not create frames it merely repeats frames. There is nothing in your television that would allow it to create frames that do not already exist.
Likewise, if your system is synched for video output to video display on a 240 Hz display it does not mean that you are magically getting 240 fps. If you are playing a game and the maximum number of times the game is rendering on your video card is 48 fps then your display is going to be repeating a lot of frames. It will still appear to be smoother, but you do not magically get more fps. This is not to say that you cannot adjust your game settings to hit 240 fps, because that is completely different.
Just don't be fooled when someone goes out and buys a 240Hz television to play games on and they report "full settings" at 240 fps. No, they're not.
