Why do we always see the same side of the Moon?

The Moon is tidally locked: it takes about as long to rotate once on its axis as to orbit the Earth once (roughly 27 days). Over billions of years Earth's gravity slowed the Moon's spin until the two periods matched, so the same face points toward us.

Small addition: we actually see a bit more than half of the surface over time, about 59%, because the Moon wobbles slightly (this is called libration).