The sky is blue because the air in the atmosphere scatters blue light. If the sky was not blue we would be looking out into space and we would see the deep black of space. This is what we would see if we were on the moon where there is no atmosphere.
We are used to seeing the blue glow of the atmosphere with the black dack drop of space. But when we look at a distant object such as a mountain range we can also see the blue light scattered in the air. This is what gives distant maontains their blue colour. When you can see rows of ranges you will notice the further away the more blue the mountains appear. This is due to the furtherest maintains being viewed through more atmoshpere, resulting in more scattered blue light.
Blue coloured mountain ranges outside Canberra, Australia.