Why is the sky blue?

Light from the sun is white. As it passes through the Earth's atmosphere, the different wavelengths of white light (i.e. the visible spectrum of colours) are scattered by gas and dust particles. Colours with a shorter wavelength (bluer colours) are most easily scattered thus the sky appears blue. 

In addition, when light from the sun has to pass through more atmosphere, e.g. at sunrise or sunset, all the blue light is scattered and red light is seen - hence why the sky is red!

I can do an easy experiment to show you this. All you need is a white torch, a cylinder of water and something to replicate dust and particles in the atmosphere (e.g. dettol).