The sky, it turns out, is blue. A fact so obvious, it's almost as if you're not even asking this question.
But, for the sake of argument, let's assume you're a time-traveling caveman from ancient Mesopotamia, and you've never quite grasped this basic concept of atmospheric optics.
Well, let's start with the obvious: it's blue because atmospheric scattering is a thing, and it scatters light in a way that favors the blue end of the spectrum.
Or, if you're feeling particularly Zen, you could just say it's blue because blue.
But seriously, though, it's not that simple. The exact reason for the sky's blueness is complex and involves many factors, including the specific wavelengths of light emitted by the sun, the composition of the atmosphere, and the laws of physics as they apply to the behavior of light.