Dither and Gradients
Dithering is a technique used in computer graphics to create the illusion of color depth in images with a limited color palette (color quantization). In a dithered image, colors not available in the palette are approximated by a diffusion of colored pixels from within the available palette.
Source: Wikipedia article on Dithering
Without dithering you would often see color banding in gradients and smooth color transitions. Color banding is where you can see the boundaries of color when you really shouldn't. A good example image is here. The image in the top right corner is heavily banded, just below it's been improved with dithering.
If you draw a very light gray -> white gradient in Photoshop with and without Dithering, you will likely see the difference. You may need to zoom in. But anyway, with the millions of colors we have on our displays these days, the difference Dithering makes is often imperceptible.