Why does the sky turn black at night?

Because the Sun is not out. The sun projects light energy and heat energy, when the Sun is not visible that means its energy isn't reaching you to the same extent. Essentially it's because the sun isn't out.

The daytime sky is blue because light from the nearby Sun hits molecules in the Earth's atmosphere and scatters off in all directions ... At night, when that part of Earth is facing away from the Sun, the sky looks black because there is no nearby bright source of light, like the Sun, to be scattered.