The rotation or revolution period is the time taken by an object to complete one rotation or revolution respectively.
The answer to this question can be explained only with the help of the following experiment.
Stand straight and hold a ball in front of your face.
Tell your friend to stand just like you, facing your front.
Keeping the ball in front of your face, turn your entire body by 90 degrees.
But your friend should not make any movements.
You will notice that, here, the ball has traveled a path of a quarter circle.
You will also notice that the part of the ball which was in the front of your friend is now on his/her right side.
This shows that the ball has turned around itself by a quarter of one full rotation.
You will notice similar phenomena if you turn by 180 degrees, 270 and 360.
This show that in fixed intervals of time, the angular displacement of rotation and that of revolution of the are equal.
The motion of the moon around the earth is same as that of the ball in the above experiment.
Hence the rotation and revolution periods of the moon are the same and as a result the moon keeps the same face turned towards the earth.