The light from the sun looks white or clear. In fact, it is actually a combination of 7 different colours of light which when mixed together appear white.
When the white light from the sun hits tiny particles in Earth's atmosphere, it is scattered in all directions. The blue light in the mix is scattered more than the other colours because it travels in shorter, smaller waves. This means it hits more particles, more often, scattering it more. With all of this blue light scattered through the atmosphere, the sky appears blue to us on Earth.
There are two parts to answer "why is the sky blue?", one of which is easier to explain to a child than the other. The idea that light is actually lots of different colours mixed together is relatively simple. Shining a torch through a glass prism, you can show children how the mix of colour is split out into a rainbow. You can also point out the blue colour in the midst of the others.
The harder part is to explain why we see only blue in the sky. For the youngest children, you can say that the sky works a bit like the glass prism. It splits the mix of colours apart, and only shows us the blue colour. As children get older, you extend your explanation to say that it is actually billions of tiny things/particles in the sky which divide the light, and show us blue.