Sometimes we see these small translucent shapes moving by when the eyes are open. When the eyes are moved they seem to follow that movement, but with a certain delay, as if they are floating in a thick viscous liquid. What is this phenomenon called?
Floaters are deposits of various size, shape, consistency, refractive index, and motility within the eye's vitreous humour, which is normally transparent.
You can read the wikipedia article to better understand the causes. These floaters are typically not microorganisms unlike you seem to think. Their scientific name is 'Muscae volitantes' and they are mostly caused due to degenerative changes in vitreous humour due to aging.
Are you referring to the "worms or strings/dots swimming on the eye/vision"-phenomenon? These are also called "eye floaters" and quite common. According to IFLscience: http://www.iflscience.com/health-and-medicine/what-those-strange-things-you-see-floating-your-eye/ they are usually harmless, but may of course cause visual annoyance.
I was unable to quickly find a scientific source, but hope this helps.
If this was not what you were talking about, I misunderstood.
What you might be referring to are white blood cells in your retina as described here: https://en.wikipedia.org/wiki/Blue_field_entoptic_phenomenon
The blue field entoptic phenomenon [...] is the appearance of tiny bright dots [...] moving quickly along squiggly lines in the visual field, especially when looking into bright blue light such as the sky. The dots are short-lived, visible for a second or less, and traveling short distances along seemingly random, curvy paths.
What you are likely seeing are tiny shadows cast upon the retina from strands of protein (and other debris) in the vitreous humor. They are indeed harmless and do correlate with age.
However, any which obscures your vision should be investigated as blood may have leaked into the eye.