I find the wikilink on visual snow accurately portrays what this looks like, and is in fact similar to how I would describe to people- like "snow" on a tv, it is a veil behind everything that we can perceive with the eye. However, I've expereienced this for as long as I can remember and it's never caused me any sort of visual problems, because it's a matter of choosing to focus on it when you want to.
I've always thought they look like circumpuncts, so if you're looking for a deeper spiritual correlation to the experience, I would start there.