The sky is blue because of the way that light of that particular wavelength from the sun gets scattered by particles in our atmosphere. This scattering means that you see blue almost everywhere you look in the sky during the day. The scientific name for this kind of scattering is ‘Rayleigh scattering’, after the British physicist Lord Rayleigh.
The sky appears blue because the atmosphere scatters light. Blue light is scattered more than the others colours, and so the sky appears blue. This is also why sunsets are red and purple. Reds scatter less than other colours, so when the light passes through more of the atmosphere (like when the sun in near the horizon), all the other colours have scattered away and only the reds are left.