A:
Suppose,
on a clear day, you look up at the sky in a certain direction. The blue light
you see is light scattered to your eye by all the molecules and all the
particles along the light's path.
If a beam strikes an air molecule or particle of dust or smoke, its blue light is three times more likely than red to scatter. The beam then re-radiates blue light in all directions, including the direction to your eye. So you see blue. See figure.
This is true for any direction you look in, except at the Sun, and that's why the entire sky looks blue.
M. McIrvin: Explains blue sky and dipole scattering
(Answered April 11, 2001; updated Sep. 21, 2007)