The moon does not change shape. It is a satellite moving around the earth. Just like earth other planets of the solar system have their own satellites that move around them. Planets also have their own orbits and move around the sun. Earth has two different types of movements. It moves around its own axis once every 24 hours. We measure time with the help of the movements of the earth. The continuous movement of the earth and the moon creates some visual illusions. It seems that the moon is slowly disappearing from the sky leading to the creation of new moon and then it slowly comes back to its full moon avatar.
The truth of the matter is that moon is a satellite of the earth which does not have its own light. The moon can be seen because the light of the sun or the reflected light of the earth falls on it and makes it visible. The moon can orbit around the earth in approximately 29 ½ days. When the earth is between the moon and the sun and all three celestial bodies are in a straight-line we can see the full moon as the side of moon facing the earth gets light from sun.
When the moon is between sun and the earth, in a straight-line, then we cannot see the moon. There are many phases of the moon like the waxing crescent, waning crescent, first quarter, last quarter, waxing gibbous and waning gibbous. The sunlight makes the moon visible but as the sunlight does not fall on the moon at an equal angle every day we do not see the same part of the moon at night. The change of shape of the moon has helped people make calendars and count time.