Here are two simple explanations:
1. For anyone:
The atmosphere is like an obstacle course for light from the Sun, and light that hits any obstacle bounces off in a random direction. Blue light tries to pass through a lot more obstacles, whereas light of other colors tries to take a more direct path and get the obstacle course over with. Since blue light ends up bouncing off a lot more often than light of other colors, it makes the sky blue.
2. For someone who is highly educated in mathematics, physics, and chemistry:
The sky is blue due to Rayleigh scattering of the Sun’s light in the Earth’s atmosphere. The amount of light scattered is inversely proportional to the fourth power of its wavelength. Out of the light coming in along the various wavelengths of the visible spectrum, blue light is on the shorter end of the spectrum, so it is scattered more efficiently than light at longer wavelengths.