Light arrives on Earth from the sun in every colour (including 'colours' we can't see like UV and infrared). When the sunlight hits the Earth's atmosphere it collides with certain particles that 'shine' blue.
Explanation: What we see as white light is actually a mix of different colours, all with a different wavelength. We see colours when a particular wavelength of light gets reflected into our eyes (the other wavelengths get absorbed or pass through an object). Our atmosphere is around 78% nitrogen; when light collides with our atmosphere, the red and green wavelengths of light pass through unobstructed. The blue wavelength is reflected by the nitrogen in the atmosphere and eventually reaches our eyes. As there is so much nitrogen, you can see the blue light from everywhere—hence the colour of the sky!
