The little specs of dust can actually be a number of small particles. They can be pollen, dirt that was moved into the air, even even bits of dead skin.
Very small and black jumping bugs look like that. They can be in all places of your house like ceiling, wall or elsewhere. They generally become more active after evening.
You most likely have dust mites, and these are small parasites that will have to be exterminated by either some kind of spray or a professional person; they're not healthy.
