When you look at some part of the sky away from the sun, the light you see from the sky is sunlight that has been scattered toward your eyes by air molecules. The sunlight induces wiggling dipoles in the molecules, causing them to emit light in directions different from the original direction of the light.

The molecules of air scatter higher-frequency light waves more strongly than they do lower frequencies. Blue light's short wavelength causes it to get scattered around 10 times more by oxygen and nitrogen molecules than the longer wavelengths (like red) of the other colors visible to us. So, to your eyes and brain, this makes the scattered light look blue rather than white.