Eric said, “I took these photos from the same hill behind my house on three different nights. If half of the Moon is always illuminated and the other half is always dark, then why does the Moon look so different on different nights?”

it is called waning and waxing It's because the moon is a world in space, just as Earth is. Like Earth, the moon is always half illuminated by the sun; the round globe of the moon has a day side and a night side. And, like Earth, the moon is always moving through space. it is also because of the position of the earth and the moon.

Explanation:

It is because the moon goes through "phases." These are the phases:

new Moon, waxing crescent, first quarter, waxing gibbous, full Moon, waning gibbous, third quarter and waning crescent. That is because the earth & moon rotate each other. Hope this helps!