As photons from the sun travel through the earths atmosphere they hit nitrogen and oxygen molecules causing them to scatter in every different direction, but not all photons scatter alike. In the mid 19th century  a physicist  named  Lord  Rayleigh  discovered that how light is scattered depends on its color. Rayleigh discovered that red light is the least likely to scatter and as we travel down the visible light spectrum toward blue and violet light, the light becomes easier to scatter. As a result, most of the blue and violet light is scattered throughout the atmosphere, while the rest of the light spectrum passes straight through.

photograph  by homepages.wmich.edu

When blue and violet photons are scattered in the atmosphere they bounce from molecule to molecule until they hit your eyes. Now from your perspective these photons appear to come from the last molecule they bounced off of, and not the sun. This makes that molecule appear blue, and since the entire atmosphere is bouncing blue photons into your eyes, the atmosphere appears blue. The rest of the light that is not scatted travels directly to your eyes from the sun, making the sun appear white.

   

 Picture from: http://spaceplace.jpl.nasa.gov/misrsky/misr-sky.htm