Overdrive is a feature that shortens the monitor response and therefore speeds up image recovery. Monitors use a voltage change on individual pixels to make it happen - the bigger the voltage change, the faster the colours change. It also depends on the accuracy with which the tension changes.
Overdrive describes when the manufacturer increases the voltage to shorten the response. As a result, the pixel on the screen gets more energy than needed to display the colours properly, which causes a slight shift in colour.