We only see one side of the Moon because it is tidally locked to the Earth. This means the Moon rotates on its axis at the same rate that it orbits around the Earth—about 27 days—so the same side always faces Earth. The Earth's gravity has gradually slowed the Moon's rotation to match its orbital period in a process called tidal locking. As a result, from Earth, we see only the "near side" of the Moon while the "far side" remains out of direct view.
Additionally, due to the Moon's slightly elliptical orbit and axis tilt, we actually get to see slightly more than half (about 59%) of its surface over time due to a wobbling effect called lunar libration, but at any given moment, only one hemisphere faces Earth.
In summary, the tidal locking caused by Earth's gravity is why we always see the same side of the Moon from our viewpoint on Earth.