The sky appears blue during the day because of the scattering of light by particles in the atmosphere. The white light from the sun is made up of all of the colors of the rainbow. Blue light is scattered more than the other colors of visible light because of its shorter wavelength. We see more of the blue light because it's scattered in many directions.
This phenomenon is called Raleigh scattering, after the British physicist Sir Raleigh. The electric field of a light wave hitting a polarizable particle causes the particle to oscillate, radiating what we see as scatted light.
The same concept explains why the sky looks orange or red at sunset. When the sun is lower in the sky sunlight must travel a greater distance to reach us. In doing so it travels through more atmospheric gas and more of the blue light is scattered before it reaches us. The longer wavelengths, red and orange, then predominate.
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