The sky is what we call the appearance of a hemisphere over our heads. On a clear day it appears blue. The deepness of the blue increases as we move from the horizon to the point above our head.

The sky is blue because of Raleigh scattering. Raleigh scattering defines the amount of scattering of light rays. Since all colors of the rainbow create a white light we should see a white sky, but blue light scatters much more than red. That is why the sky appears blue (on a cloudless day).

On a cloudy day, it appears to be grey.

In other rwords, the sky is blue for the same reason that everything that is blue looks blue, like blue ink or a blue shirt. You may think that air, the main sky / atmosphere component, is transparent but thick layers of air - a few kilometers or miles, like the atmosphere's width, are bluish due to small dust perticles. So the sunlight that passes the atmosphere air reaches your eyes blue like a beam of bright like passing some blue glass or filter.

But why are sunsets and sunrises red? Because at sunset times the atmosphere air is red? To understand this you may need some more advanced explanation described in the following chapter.

See also: Why is the Sky Blue - Experiments, Demonstrations and Background

Source: Wikipedia (All text is available under the terms of the GNU Free Documentation License)