The left side of the image is a 4-shade non-dithered image; the right side is a 4-shade image WITH dithering
When few colors are available, dithering preserves more nuances than a non-dithered image, but the trade-off is a "dirty," speckled look. Some dithering algorithms are better than others; the one I've used falls somewhere in the middle, which is why I selected it.
As a final example, here is a 16-color grayscale image with full dithering, followed by a side-by-side comparison with the non-dithered version: