Why is the refresh rate of most LED LCD TVs 60Hz?
NTSC television refreshes at approximately 60 half-frames (i.e. it uses interlaced video) per second. Using the same rate (or a multiple thereof) for LCD TVs simplifies the electronics since it can just toss the whole frame onto the screen at the right time and then move on to dealing with the next frame.

Higher refresh rates can work one of two ways:


Duplicating a frame for the full duration that it should be shown, such as having a 240Hz display show a frame 4 times when working with a 60fps source.
Performing image analysis to tween from one frame to the next, i.e. analyzing two source frames in order to interpolate motion for the additional frames created in between due to the higher refresh rate of the TV


The former method uses the source's native rate, whereas the second simulates the higher rate of the TV through digital trickery.