Consider the case of a 1-bit image. Let's say the "signal" is a smooth gradient of black to white from one side of the image to the other. If you simply quantize to the nearest value, one half of the image ends up solid black and the other half, solid white. No amount of after-the-fact "dithering" of this image will recover the original gradient - it is lost forever.

Now supposing we add noise to our signal before we quantize. A given pixel at 25% gray (which under the previous scheme would always end up solid black) now has a 25% chance of ending up white. A contiguous block of such pixels will have an average value of 25% gray, even though an individual pixel can only be black or white. Thus, by flip-flopping between the two closest values ("dithering") in statistical proportion to the original signal, information is preserved.

https://en.wikipedia.org/wiki/File:1_bit.png