How has the structure of human and animal eyes influenced how they live?

Rather than the structure of our eyes influencing the way we and animals live, it would be more accurate to say the way we live/the way we engage with our surroundings has influenced the way our eyes are structured. 

Human eyes are adapted for creatures living in tall grass-lands and forests where differentiation between distance, color, and movement were crucial to our survival as a species. Unlike many animals that lived in a similar environment, our eyes and brains became adapted to finding movement and differences in color which allowed us to spot predators that may have been camouflaged in the tall grasses. Our eyes, however, didn't need to see extreme differences in color or even different wave-lengths, such as mantis shrimp which can see ultraviolet light, or raptors whose eyes are extremely specialized for spotting very small prey from hundreds of feet in the air. This leaves us being very good at detecting the "average" spectrum of red, blues, and greens, but not much else.

Animals had to make similar adaptations. Many predatory fish, for example, rather than develop extremely detailed vision, swim low and look upwards using the light trickling down from the surface. If they see a shape moving that is a different color than the surface, they will investigate. On the other hand, most deep sea fish have eyes that have no cone capable of detecting red light, as red light is the first wavelength to completely disperse in the upper waters and won't make it into the deep oceans. Some predatory fish use this to their advantage and have specialized red glowing anglers that only they can detect, leaving their prey shining brightly and completely unaware. 

To recap, the way our eyes and brains interpret light do have an effect on the way we live, but our environments and the way we and other animals survive has had much more of an impact on the way our eyes worked best. Evolution has guaranteed most species the best eyes possible for each of their unique survival conditions. Hope this helped!