Most atmospheric particles are so called Rayleigh-scatterers. The particle size is small compared to the wavelength of visible light. These molecules of the air favour the scattering of small wavelengths, i.e. the blue part of the spectrum, whereas the reddish light is mostly unaltered. The blue light is scattered by the air particles into our direction and our eyes, whereas the red light just goes straight through. This makes the usual daytime sky blue.

Furthermore the blue color appears brighter and less saturated close to the horizon and close to the sun, whereas it is exceptionaly dark and saturated at an angle of about 90 degrees from the sun (on the line trough the sun and the zenith). The brighter sky low above the horizon is caused by the larger number of air particles and in addition by the presence of aerosols. The aerosols are particles with larger sizes than the usual air molecules. Scattering the light, the aerosols don't favour any wavelength (Mie-scattering). Thus the colour is less saturated at low elevation angles.
The favoured forward scattering of the small Rayleigh-scatterers and additionally the larger aerosols makes the sky brighter and less saturated close to the sun. The minimum of Rayleigh-scattering is at the angle of 90 degrees.

References:

• Hoeppe, Götz, Blau - die Farbe des Himmels, Spektrum Akademischer Verlag, 1999
• Minnaert, M.G.J., Light and Color in the Outdoors, Springer-Verlag, 1995
• Gibbs, Philip, Why is the sky blue?, 1997