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 it goes through. One of which will be displayed.
Similarly, you will see the Sunrise and Sunset times displayed on the graph.
It will tell you current day hours the sun is visible from sunrise to sunset, and the night hours from sunset to sunrise.
This information is directly related to the current location you have selected.