Light is made up of waves of different sizes called wavelengths. The short waves look blue. Our atmosphere is like a blanket made up of gases and particles that wraps around the Earth. When sunlight hits our atmosphere, the light waves scatter in all directions … especially the short blue ones. 

We see different wavelengths as different colors. Sunlight looks white, but it’s really every color of the rainbow. Bigger, longer waves look red to us. Smaller, shorter waves look blue, as you know. We can’t see these different colors until something bends light (like a prism), reflects it (like a mirror), absorbs it (like red sneakers) or scatters it (like the atmosphere). Since shorter waves are easier for the atmosphere to scatter, the sky looks blue. 

Our eyes can only see a few of the colors in the entire universe, and sky blue is one of them! The colors we can see are called visible light. But most light in the universe is invisible to our eyes. It shines at wavelengths we can’t see without special instruments. These other wavelengths include gamma rays, X-rays, ultraviolet radiation, infrared radiation, microwaves, and radiowaves.

For fun further reading, check out NASA's answer to this classic question. It features helpful illustrations.