You will see the Moonset and Moonrise times displayed. After Moonset, it dips below the graph showing the moon is not visible in the sky. After Moonrise you will start to see it rising up from the horizon, like in the graph.

In the top right you will see the current phase of the moon.

These are all the phases the moon goes through. One of which will be displayed.

Similarly, you will see the Sunrise and Sunset times, Civil Twilight and Nautical Twilight displayed on the graph.

Sunrise and Sunset times tell you the current day hours during which the sun is visible from sunrise to sunset, and the night hours from sunset to sunrise.

Civil Twilight: The period when the sun is just below the horizon (0–6°). It’s still light enough for most outdoor activities without artificial light.
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Nautical Twilight: When the sun is 6–12° below the horizon. It’s darker, but the horizon is still faintly visible to the naked eye at sea.

This information is directly related to the current forecast location you have selected.