What is the difference in perception of polarized light and unpolarized light? What difference does polarized light cause to our eyes?
Our eyes cannot see any difference between ordinary (i.e., unpolarized) and polarized light. You can check it yourself, if you look through a polarizer (for example, some sunglasses have one). All you can notice is that the world gets slightly darker (because you block roughly half the incoming light). In addition, some reflections might be reduced dramatically (that is, after all, one of the main points in using polarizers in sunglasses).
There are, however, other species (e.g., bees, as far as I know) that can see the difference but, unfortunately, nobody has been able to ask them what such a difference looks like...
There is some evidence of polarization perception.
Many people are able to perceive polarization of light. It may be seen as a yellowish horizontal bar or bow-tie shape (with "fuzzy" ends, hence the name "brush") visible in the center of the visual field against the blue sky viewed while facing away from the sun, or on any bright background. It typically occupies roughly 3–5 degrees of vision, about the same size as the tip of one's thumb held at arm's length. The direction of light polarization is perpendicular to the yellow bar (i.e., vertical if the bar is horizontal). Fainter bluish or purplish areas may be visible between the yellow brushes (see illustration). Haidinger's brush may also be seen by looking at a white area on many LCD flat panel computer screens (due to the polarization effect of the display), in which case it is often diagonal.
See, for instance, Haidinger's brush on Wikipedia.