On a bright, sunny day, the sky appears blue to us as we look up. Notice the word appears here. The sky is not actually blue, but the blue color results from the way the sunlight is scattered when it hits air molecules in the earth's atmosphere.
Sunlight looks white to us, but it is actually composed of all the colors of the spectrum or rainbow. Light is transmitted in waves, and various colors of light move in different ways. Red light, for instance, travels in long waves with peaks that are rather far apart. As we move through the color spectrum, the wavelengths of the light get shorter and shorter. Orange has shorter waves than red, yellow than orange, and green than yellow. Blue has the shortest wavelengths of all.
When light hits the atmosphere, it scatters, bouncing off air molecules, gasses, and other particles. Blue light, with its short waves, bounces more than any other color of light, and it scatters everywhere, more quickly, more intensely, and more widely. In fact, blue light is scattered in all directions about ten times more than red light is. This makes blue light more visible to our eyes. It is bouncing around all over the place, and it essentially calls our attention to itself. Therefore, the sky appears blue from that active blue light.
Notice, though, how as we look toward the horizon, we usually see more white in the sky than any particular color (at least during the day). By the time the light gets down so low in the sky, it has bounced around and scattered so much that all the colors mix back together. One does not stand out in particular anymore, and that is why we see white.