... like I'm 5 years old
The sky appears blue to us because of a process called scattering. Imagine the sky as a giant, invisible bubble. When sunlight, which is made up of different colors, enters this bubble, it collides with molecules and tiny particles in the air. The light then scatters or spreads out in different directions.
The blue color comes into play because sunlight is a mixture of colors. And each of these colors is associated with a different wavelength. Some colors, like red, orange, and yellow, have longer wavelengths. Others, like blue and violet, have shorter wavelengths. During the scattering process, colors with shorter wavelengths get scattered more than those with longer ones. That's why we see a blue sky instead of a red, orange, or yellow one.
Think of the sky as a big, invisible sieve. When you pour a mixture of different sized grains into this sieve, the smaller grains (like our blue light) will get through more than the larger ones (like the red or yellow light).
... like I'm in College
Going deeper into the science, the sky appears blue due to Rayleigh scattering, named after the British scientist Lord Rayleigh who first studied it in detail. In this process, when sunlight (composed of different colors each with a distinct wavelength) hits the molecules and tiny particles in the Earth's atmosphere, the light is scattered in multiple directions.
However, not every color scatters equally. Rayleigh scattering is more effective for light with shorter wavelengths. As blue and violet light have the shortest wavelengths in the visible spectrum, they are scattered more. But here's a twist: while violet light gets scattered more than blue light, our eyes are less sensitive to violet light and the sun emits less violet light to begin with.
Besides, some of the violet light gets absorbed by the ozone layer. The combined effect of these factors makes a clear daytime sky appear blue instead of violet.
Imagine you have a box of Lego bricks of different colors and sizes. The smaller bricks represent shorter-wavelength light like blue and violet, and the larger bricks represent longer-wavelength light like red and yellow. Now, imagine pouring these Lego bricks into a large container with small holes at the bottom.
The smaller Lego bricks (blue and violet light) will fall through the holes more easily and in greater quantity than the larger Lego bricks (red and yellow light). Similarly, in the Earth's atmosphere, the smaller 'bricks' or shorter-wavelength light is scattered more, making the sky appear blue.
However, just like our eyes are better at noticing certain Lego colors over others, they are more sensitive to blue light than violet. So, even though more violet 'bricks' might pass through the holes, we perceive the scattered 'bricks' as largely blue because our eyes are more receptive to that color.
... like I'm an expert
For an expert's perspective, we delve deeper into the principles of Rayleigh scattering. The intensity of scattered light relies on the inverse fourth power of its wavelength, a principle stated mathematically as I ~ 1/λ^4. Hence, light with shorter wavelengths (blue and violet) is scattered exponentially more than light with longer wavelengths (red, orange, and yellow).
However, the perceived color of the sky is also influenced by human physiology. Our eyes contain two types of photoreceptor cells - rods, which are more light-sensitive and cones, which are more color-sensitive. Cones are further divided into three types, each sensitive to short (S), medium (M), and long (L) wavelengths. Our eyes' sensitivity peaks at the M and L cones, which correspond to green and red respectively, but the S cones, which correspond to blue, are less sensitive.
Moreover, the Sun's spectral irradiance is less in the violet range, and the ozone layer absorbs a significant amount of violet light. Hence, despite violet light being scattered more, our eyes perceive the sky as blue.