Think about shooting with a shotgun at a target. If you have a thousand pellets, the distribution of pellets at the target will be quite smooth. Now, shoot through a narrow aperture that takes out 99% of the pellets. Now you have ten pellets. The distribution can not be smooth. The sampling frequency (pixel size) at the target does not matter much. It is the aperture size.

I realize that is a very flawed analogy but it's the quickest I could come up with.

Here's more: http://en.wikipedia.org/wiki/Shot_noise#Optics