Moon is a natural satellite of earth but life on the moon is not possible as on the earth because of many reasons.
Firstly there is no water on the moon which is the first and foremost requirement for the life. Life first started on the earth because of water and if no water we can imagine no life.
Air is also required to breathe and no air is on the moon or we can say that oxygen is required by human beings to breathe is not enough on the moon for the survival.
Moreover the temperature on the moon is not suitable for the life to exist. Other than these basic needs there are more reasons because of which life is not possible on the moon such as the angle at which the moon is tilted, its speed of revolution around the sun, speed of its rotation around its own axis and distance from the sun etc.
Earth is the only planet that fulfills all these conditions to make life possible whereas many of these conditions are not fulfilled by the moon and hence there is no life.
But nowadays a question arises that whether aliens also needs the above mentioned conditions. It is possible that they can live without air, water and atmosphere and can make life possible but still no such alien or civilization is found yet on the moon.