Light is what's called an electromagnetic wave. It pulls any particle that has electric charge back and forth as the wave passes by, sort of the way that a water waves pushes things up and down as it passes by. These waves pull back and forth on the electrons in the molecules in the air, because the electrons have electric charge. When the electrons move back and forth, they send out new waves, spreading out in all directions. Those waves are the light we see from all parts of the sky.
Light from the sun is white, which means it's made up of a whole range of different colors. Each color corresponds to some rate at which the electric field wiggles back and forth. Blue is the fastest back-forth wiggle we can see, red the slowest. We say blue is the highest frequency and red is the lowest frequency.
So why does the high frequency blue light get scattered around by the air more than the low frequency light? The reason has to do with how the moving electrons respond to the waves and radiate new waves. Because the electrons are not heavy and are stuck tightly in their molecules, the distance that they wiggle depends only on the strength of the wave hitting them, not on its frequency, at least for visible light. For a given distance of wiggle, you get more radiation the faster the wiggle happens. So the high frequency blue light scatters more, and that's mostly what you see coming from the sky on a clear day.
It's actually a bit more complicated if you worry about details (like physicists do). If you are interested, have a look atthis nice webpage.
Mike W. (with a link from EJ)
(published on 10/22/2007)