What makes the sky look blue?

Air molecules scatter light, and they scatter short wavelengths far more strongly than long ones - the effect goes as the fourth power of the frequency, so blue is deflected something like ten times as much as red. Sunlight arriving at the top of the atmosphere is close to white; the blue part of it gets bounced around the sky in all directions, so it reaches your eye from everywhere rather than only from the direction of the Sun.

The same fact explains sunset. Low in the sky, light travels through far more air to get to you, and by then almost all the blue has been scattered out sideways. What is left to arrive directly is the red and orange end of the spectrum.

Two loose ends worth tidying. Violet is scattered even more strongly than blue, so the sky ought to look violet - it does not, because the Sun emits less violet and our eyes are much less sensitive to it. And the sky is not blue because it reflects the sea; the sea is largely blue because it reflects the sky, and because water itself absorbs red light over depth.