Why is the sky blue?

The blue sky is a result of the diffusion of sunlight by the atmosphere. If it did not exist, we would see an all-black sky and the stars would be visible in daylight.

The white light of the Sun is a mixture of all colors of the rainbow sky. Light travels in waves of different lengths. Each color has its own wavelength. The light then travel in a straight line until it encounters an obstacle that the returns in another direction. When the solar rays enter into the atmosphere, they encounter the atoms, the molecules of air, water drops and the dust which comprises the atmosphere. Air molecules have the correct size to disseminate the shorter wavelengths of light, violet, indigo and blue in this case; longer wave lengths, such as red, are almost not broadcast by these air molecules.

So it's a blend of violet, indigo, blue, green and a small fraction of other colors that are broadcast across the sky, giving it the blue that we know well.