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This essay is not intended to explain the exact way a LCD panel works, I assume people reading this are familiar with the basics of LCD operation. If you don't here is a good introduction to the operation and construction of LCD panels:

History of TFT LCD

But since the text talks about black, white and gray pixels a reminder that the entire screen is made up of three b/w pixels with a color filter for each pixels. Therefore, a gray-gray transition could be also thought of as one color or shade to another.

LCD Pixel Response Time.
One of the most important specifications for a LCD panel is the pixel response time. In the early days of LCD panels used for video and computer monitor applications, sported a pretty slow responding pixel response. To Illustrate the difference here is an example:

     Slow Pixel Response

     Fast Pixel Response

From: Viewsonic White Paper

To understand what is going on it is necessary to look at what is happening to the LCD panel as illustrated here:

From: Viewsonic White Paper

Notice the Falling Transition describes the time required for the pixel to go from full luminescence to minimum luminescence and the Rising Transition describes the time required for the pixel to go from minimum luminescence to full luminescence. The combination of these two times is the pixel response time for a white-black-white (w-b-w) transition. That is one method of reporting pixel response times used by some manufacturers.

But that does not tell the entire story. It turns out when the pixel is excited by the full input voltage to turn the pixel dark, it also will respond the fastest because of the driving force. Conversely, when the pixel voltage is reduced to the minimum it also will respond the fastest. But when an intermediate transition occurs, say one level of gray to another level of gray (such as encountered with video) the driving force is much less and the pixel will respond slower. It not uncommon for this gray to gray response to take up to 120 ms for a LCD that is rated at a 25 ms w-b-w response time. Using a conservative ratio of 3:1 you could extrapolate an 8 ms LCD to 24 ms. 

From PC World article:
VESA has a technical definition for rise-and-fall, but the gray-to-gray spec remains undefined. Industry experts agree that in LCDs, transitions between the fine distinctions of gray-to-gray are 3 to 4 times slower than those of rise-and-fall. "The voltage required to turn something from black to white or white to black is greater, so it's faster. Controlling the voltage from gray to gray makes it slower," says Samsung's Nichols.

A ViewSonic representative uses a car analogy to explain the same point. "Fully off is a black image, fully on is a white image. It's similar to a gas pedal on a car--you're either off or on. But this spec doesn't cover all the speeds in between off and full throttle. Gray-to-gray is typically slower because it's in smaller differences that aren't normally overdriven," says Erik Willey, senior product manager for LCD at ViewSonic.

Newer technologies have fortunately reduced not only the b-w-b response time, but have also reduced this ratio as well, but the difference between w-b-w and gray-gray response times still exist, so it is important to know what response time the manufacturer is reporting and if they just say “response time” you can bet it is probably the w-b-w time since it will make the LCD look the best.

So How Fast Is Necessary?
Here we need to review what is required to form a picture on a LCD screen. With a 60 Hz refresh rate that would fully paint a new picture 60 times per second, the maximum response time for each pixel can be easily calculated. Take the popular 1366x768 resolution (I'm not going to dwell on SD resolutions here) there are a total of 1,049,088 pixels. Refreshed in 1/60 sec will require .0167 seconds or 16.7 ms. If you step up to the 1920x1080 resolution, there are a total of 2,073,600 and will take the same 16.7 ms. The reason both require the same time is the pixels are all virtually updated at the same time as opposed to a CRT pixel that is scanned one after another.

So the minimum desired response time is going to be 16.7 ms or 20 ms if using PAL 50 Hz video. Now bear in mind these are gray-gray numbers.

Black Frame Insertion (BFI)
One of the benefits of the faster response time is the ability to incorporate what is called black frame insertion. By inserting a black frame in between the normal video frames, not only does the overall response of the pixel improve because the gray to black and back to gray will occur faster than gray-gray transitions in these fast LCDs, but the inserted black frames between the picture frames allows for improved black levels approaching those available with a CRT. So right there you can see the value of a 8 ms LCD since the frames will be doubled requiring a 120 Hz screen update. On some slower responding LCDs this black frame is inserted by turning off the backlight rather than just the LCD pixels.

In Plane Switching (IPS)
This technology first introduced by Hitachi in 1995 was developed to increase the viewing angle of LCD panels. It features a LCD cell that has both electrodes on the same plane or substrate. The downside of IPS is a slower response time, but that has somewhat been overcome by the newer technology fast LCDs. For more details on this technology see:

In-Plane Switching

Some manufacturers will advertise the new Super IPS as improving response time, but it is not due to the IPS technology, but it rather due to the faster LCD panels. LCD that combine the 8 ms pixel response times with IPS provide a fast display with a large viewing angle, typically 170 degrees, or more, both horizontally and vertically.

Additional References:
PC World: LCD Specs: Not So Swift