It is really interesting how the eye is able to take light, bend it and reassemble the information into an object. Here is the basics of how it all works.
Being able to see all comes down to how the eye is able to focus light. As light enters the eye through the cornea (the outer part of the eye), light begins to bend. This is begins what is called "refraction." After light goes through the cornea, it bends one more time by a crystalline lens inside the eye as it goes to the retina, where the light is focused. Once the light is focused, it stimulates cells that send millions of electrochemical impulses along the optic nerve to the brain. The brain uses a special section near the back that interprets the signals into an image of an object. The amazing thing is that this complicated process happens automatically and in less than a blink of an eye.
However, sometimes the eye has trouble focusing light. Vision becomes blurry and objects don't appear as sharp anymore. That is where the importance of an eye exam and corrective prescription like glasses or contact lenses come to the rescue. It can adjust the focus of the light so that the eye and brain can clearly define objects. During an eye exam with an eye doctor, one of the technicians will use what is called an auto-refractor. It measures the approximate amount of correction is needed and tells the optometrist if there is an astigmatism or not.
What about animals? Well, they aren't exactly your typical eye exam patient, but I did dig up this YouTube video of what was just explained and how humans and animals see the world in sometimes different lights.