Short answer: The sky is blue because blue has shorter wavelengths and higher frequencies than red on the visible spectrum.
To understand why the sky is blue, we first need to understand how sunlight interacts with the molecules in our atmosphere. Sunlight looks white to the human eye. Think of sunlight as an electromagnetic wave that causes the particles inside air molecules to oscillate up and down, as sunlight passes through the atmosphere.
When this happens, the oscillating particles produce electromagnetic radiation at the same frequency as sunlight. The radiation spreads in different directions. This redirecting of incoming sunlight by air molecules is called scattering.
Blue has shorter wavelengths and higher frequencies than red on the visible spectrum. Thus, as the sunlight of all colors passes through air, the blue light causes charged particles to oscillate faster than does the red light, so the blue light is scattered more strongly than red light across the sky, making the blue more visible. This is why the sky appears blue.