Answer:
This is very sensitive topic, especially after Apple had a lot of lawsuits because of they 6-bit LCD panels in their laptops. I am going to use this Apple example to describe what exactly dithering is.
To make pixel on the screen to show some specific color we are suing RGB (Red-Blue-Green) color model. By mixing these three colors we can make pixel show any color we want. Apple did use 6-bit LCD panels, which means that each of three channels (R, G, B) will be encoded in 6-bits. So, each channel could have a value from 0 to 26 (64), it means that we could have 643 (262144) different colors. Apple did advertise that they support millions of colors, that is basically achieved by using 8-bit LCD panels which allows 16777216 different colors.
It looks that Apple is not able to handle millions of colors by hardware, but here comes the dithering (in printing there is very same technique, but called Halfone). Dithering is software way, which allows you to have millions of colors by combining two different colors from pixels-neighbors. Human eye is not capable to see one very small pixel, you understand some group of pixels. Those two or several pixels blurs to some new color.
For example image a chess board. There are two colors of squares: blue and red. If I would take that one pixel is one square (You hardly can see one pixel with your eye) overall you would see a violet colored square (our chess board, which you will not be able to identify anymore as chess board).