Daylight draws the terminator on a map of the world, and shades in the areas of the world where it's night - by default, it draws the current terminator, but you can specify the exact time for which the terminator should be drawn.
If you want to see in more detail, turn your device sideways for a scrollable, zoomable map.
There's a selection of maps to choose from (using the Settings application).
Daylight determines your current location and uses that for the initial position of the zoomed in map.
