Rayleigh Scattering Makes the Sky Blue.
Rayleigh scattering (pronounced "Ray-Lee") is the light phenomenon that makes our skies blue. When sunlight passes through the atmosphere, light beams encounter tiny bits of dust on their way to the ground. These particles absorb energy from the incident light, vibrate, and then re-emit the light, scattering it in all directions. All colors are scattered by these atmospheric particles, but blue (and violet) are selectively scattered the most. This phenomenon of selective scattering is termed "Rayleigh scattering." The sky is blue because we see the scattered blue light that reaches our eyes. (The sky doesn't look blue-purple because our eyes are more sensitive to blue light and because the sun emits more energy as blue light than as violet.)
In the evening, the sun's rays (especially those on the horizon) must go through a thicker slice of atmosphere before it gets to our eyes. More atmosphere means more molecules to scatter the violet and blue light, and if the path is long enough, then all of the blue/violet light will get redirected out of our line of sight. However, yellow, orange and red light (which are less scattered) will continue along a straight path between the sun and our eyes. This is why we see red skies in the evening.
Don't Believe Me?
Here's a simple experiment you can try at home - all you need is some milk, a clear glass cup, and a flashlight. Pour some water into the glass cup and shine the flashlight through the sides of the glass. The water should be clear. Now, add milk to the glass, one drop at a time, while keeping the light shining through it. Milk contain tiny molecules of protein and fat which are around the same size as atmospheric dust, and these particles scatter blue light in similar fashions.
After adding a few drops of milk, the light beam passing through the water/milk mixture should become visible (the light is scattered/reflected off of the protein/fat particles and returns to your eyes so that you can see it). After a few more drops, the mixture will turn a distinct blue color. If you don't notice the blue tint at first, you can convince yourself that blue is indeed scattered by putting a piece of paper behind the glass container to observe the outgoing flashlight beam. The exiting beam should be orange on the paper, proving that all the blue light was scattered out, leaving only the colors of red, orange and yellow (much like during a sunset).
Still Don't Believe Me?
Walter Lewin, one of my favorite MIT professors demos this effect in a youtube video found here. (From 57:20 1:02:40) Using fine-particulate from cigarette smoke, he turns incident white light blue. This is exactly what happens in our skies!