The sky appears blue because the sunlight is scattered in the earth's atmosphere. Sunlight itself consists of different colours, which together appear white. Each of these colours has a different wavelength, and blue has a shorter wavelength than red or yellow.

In the atmosphere, the light rays hit molecules and tiny particles. This scattering of light works according to the Rayleigh scattering principle, which states that light with shorter wavelengths (such as blue and violet) is scattered more strongly than light with longer wavelengths (such as red). Because blue and violet are so strongly scattered, we see the sky in these colours.
Interestingly, violet light is also scattered, but our eyes are more sensitive to blue and the atmosphere absorbs violet more strongly. This is why the sky appears predominantly blue to us.