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Overdrive is an optional setting built into some monitors which lowers the response time of the pixels on the display. This lowers the time taken for each pixel to update from one picture to another, reducing any ghosting or motion blur present in games or high motion media such as sports.
Overdrive also can be used to make objects in motion appear more crisp in general for casual or professional use.
Overdrive can be enabled by pressing the menu button on your monitor to bring up the On-Screen Display (OSD). This setting is typically named response time, overclock, overdrive, or trace-free, however it depends on the manufacturer of the display.