You're actually asking about why we see different phases of the Moon, not why we only see a quarter of it.

Here's the explanation:

* The Moon doesn't produce its own light. It reflects sunlight.

* The Moon orbits the Earth. This orbit takes about a month to complete.

* The Sun illuminates half of the Moon at any given time.

* The angle between the Sun, Earth, and Moon changes as the Moon orbits. This changing angle causes us to see different amounts of the illuminated half of the Moon, creating the phases.

Here's a breakdown of the phases:

* New Moon: The Moon is between the Sun and Earth, so we see the unlit side.

* Waxing Crescent: We start to see a sliver of the illuminated side.

* First Quarter: We see half of the illuminated side, like a quarter of a circle.

* Waxing Gibbous: We see more than half of the illuminated side.

* Full Moon: The entire illuminated side faces Earth.

* Waning Gibbous: We see less than half of the illuminated side.

* Last Quarter: We see the opposite half of the illuminated side, again like a quarter circle.

* Waning Crescent: We see a shrinking sliver of the illuminated side.

So, we don't see only a quarter of the Moon, we see different amounts of the illuminated half depending on its position in its orbit.