Motion rate refers to the number of frames per second that a TV is capable of displaying. The higher the motion rate, the "smoother" the motion is going to be for the TV.
However, it's really debatable whether or not there is any noticeable difference between watching TV in 60 Hz or 120 Hz. The only situation where you should really care about it is if you're using your TV as a monitor for a gaming PC. High-end gaming PCs that play games at higher than 60 FPS will experience visual artifacts and "screen-tearing" if you try to play them on a monitor that's incapable of displaying the frames as fast as the system is feeding them. You'll be fine playing on consoles, because they don't play any games at higher than 60 FPS.