Transmitted light (from the sun, light bulbs, fire, etc) is made up of a spectrum of colors. The longest wavelengths of light are on the red end of the spectrum and the shortest wavelengths are on the blue/violet end of the spectrum.

When transmitted light such as sunlight enters our atmosphere it collides with the oxygen and nitrogen atoms. The color with the shorter wavelength is scattered more by this collision. Because violet and blue are the shortest wavelengths the sky appears to be violet / blue. But because our eyes are more sensitive to blue light than they are violet light, we perceive the sky as blue.

Taken from why-is-the-sky-blue.tv