Why do eyespots develop and what is the environmental advantage of an eyespot? I am curious about this because the human eye is so complex in and of itself, but you also need the processing power of the brain to have it all come together. What's the value of a partial eye?
A single cell organism uses its eyespot to guide it towards light (where it can photosynthesize). This is a purely mechanical process, since they do not actually see. Light activates motor proteins that cause the flagellum to whip around, and the eyespot detects the direction with the highest light level, which activates other motor proteins that change the direction of movement.
Even in humans, not all light-sensing is mediated through the eye. We also have photoreactive chemicals in our skin. Tanning, for example, occurs as a result of light exposure.
Spiders and other creepy crawlers have tiny brains, and they do not process images much at all. Still, they respond to movement and levels of light. Despite their rudimentary vision, jumping spiders are pretty good at launching themselves unerringly towards their prey.
Other animals see far better than we do. For example, birds devote most of their brain to image processing, and they see orders of magnitude more detail than we. However, their eyes do not swivel in their heads--that is why they bob their heads when they walk.
Plants also respond to light through photoreactive chemicals. They have no vision whatsoever.