When we look at the Moon in the night sky, why do we always see the same side every night?
The Moon is Tidally locked to the Earth.
This effect is known as synchronous rotation. A tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces the Earth.
We have a few questions centering around the concept of tidal-locking you may want to take a look at them.
Because of tidal locking. The gravitational forces between two massive bodies like the Earth and the moon will cause their rotations to slow down over long periods of time, eventually stopping them relative to one another.
The smaller body will lock first because the larger body's gravitational effect is stronger, but at some point in the distant future, Earth's rotation will slow to once a month as well, showing the same face to the moon at all times.