Short answers, pulled from the story.
An eye is a sensory organ that lets an organism perceive visual information by detecting light and converting it into electro-chemical impulses in neurons. In higher organisms it collects light, regulates its intensity through a diaphragm, focuses it through lenses to form an image, and transmits the resulting electrical signals to the brain through the optic nerve.
Eyes with resolving power come in ten fundamentally different forms, sorted into compound eyes and non-compound eyes. Compound eyes are made of many small visual units and are common in insects and crustaceans, while non-compound eyes use a single lens and are common in mammals, including humans.
The common origin of all animal eyes traces to a proto-eye believed to have evolved some 650 to 600 million years ago, with the PAX6 gene considered a key factor. The first proto-eyes appeared around the time of the Cambrian explosion.
The mantis shrimp has the world's most complex colour vision system, with detailed hyperspectral colour vision. Some compound eyes carry up to 28,000 sensors arranged hexagonally, which can give a full 360 degree field of vision.
Compound eyes comprise many individual lenses laid out on a convex surface, while simple eyes have one concave photoreceptive surface. Compound eyes offer a very large view angle and detect fast movement but have much lower acuity, since the physics of compound eyes prevents resolution better than 1 degree.
Rods cannot distinguish colours and are responsible for low-light monochrome vision using the pigment rhodopsin, which is sensitive at low light intensity. Cones are responsible for colour vision and require brighter light, and in humans there are three types maximally sensitive to long-wavelength, medium-wavelength, and short-wavelength light.