What is overdrive?
Pixels on an LCD do not switch states instantly. Moving a pixel from gray to another gray takes time - this is your monitor's response time. During that transition, the pixel exists in an intermediate state, creating a ghost trail behind fast-moving objects.
Overdrive (also called Response Time Overdrive, AMA, TraceFree, or MPRT depending on the brand) applies a higher voltage pulse during the transition to force the pixel to switch faster. Without overdrive, a pixel gets a "normal" voltage. With overdrive, it gets a boosted voltage that pushes it past the target faster.
The overshoot problem
The tricky part is stopping at the right value. If the overdrive pulse is too aggressive, the pixel overshoots - it goes past the target gray value, then has to correct back. The visual result is inverse ghosting: a white or bright halo appears in front of a dark moving object.
Inverse ghosting is often more visually distracting than regular ghosting because it appears ahead of the object, which your brain is not trained to dismiss.
The typical settings
Most monitors offer 3–5 overdrive levels. The naming varies by brand:
How to find the right setting
The correct overdrive setting depends on your current refresh rate. A setting that is perfect at 240Hz may cause severe inverse ghosting at 60Hz. If you use adaptive sync and your framerate fluctuates, adaptive overdrive (available on some G-Sync modules) automatically adjusts the overdrive pulse to match the current refresh rate.
Test with the Motion Blur Test on this site. Set a medium overdrive and look for ghost trails behind moving objects. Increase until ghosting disappears, then back off one step if you see a bright halo appear.
OLED monitors have no overdrive
OLED pixels transition essentially instantly (sub-millisecond). They do not need overdrive and do not have the smearing issues that plague LCD panels, especially VA.