It's because Earth pulls on the bulge in the Moon created by Earth's gravity.

It has to do with the tides. Except in this case it isn't ocean tides - it's lunar tides. Just as the Moon's gravity creates a bulge in Earth's oceans, Earth's gravity creates a bulge in the material that makes up the moon.

If Earth and the Moon didn't rotate, the bulges would "point" directly at the other body. But with rotation, the tidal bulge is a little bit offset in the direction of rotation. And the Moon used to rotate.

That offset creates a torque. Earth's gravity tries to pull the bulge into perfect alignment. Over time this slows the rotation of the moon until it stopped rotating at all.

(Technically the Moon does rotate, but it does so at the same rate that it orbits Earth. So it doesn't rotate from our perspective.)