Dithering is a trick many graphic applications use to fool your eye into seeing a whole lot more colors (or grey tones) on the screen than are really there. The computer achieves this optical illusion by mixing together different colored pixels (tiny dots on the screen that make up an image) to trick the eye into thinking that a totally new color exists. For instance, since pixels are so tiny, if the computer intermingles a series of black with white dots then you're going to think you're seeing gray.
Color dithering smoothes out images by creating intermediate shades between two more extreme colors (called a blend). Dithering also makes the best use of the limited number of available colors, like when you open a 24-bit color image (millions of colors) on a computer that's only capable of displaying 8-bit (256 colors).
There is a half tone effect for black-and-white images called dithering. Rather than dots of varying sizes, a dithered image has dots or squiggles all the same size, arranged in such a way as to create the illusion of gray values