The moon changes its shape everyday over a period one month and this repeats over and over again. These different shapes of the moon are called 'Phases of the Moon'. In reality, the moon does not change its shape at all. Moon is always round in shape. As we know the moon is always visible because it reflects the light from the sun.
It goes from a perfect round circle and gradually reduces in size and further becomes a no moon (as shown here). This takes about 15 days. This is called waxing.
Then the moon again begins to grow in size until it becomes a full moon. This takes another 15 days. This is called waning.
The total span between 2 full moons is approximately 30 days nearly a month.
At any point of time, the sun is able to illuminate only half part of the moon. The other half of the moon does not receive any portion of sunlight because of its spherical shape.
Depending on the these positions of sun, moon, and the earth, different proportions of the illuminated moon faces the earth, causing the shape of the moon appearing to change as seen from earth.
On a full moon day, when the moon appears as a bright complete circle, the earth is directly between the moon and the sun. The illuminated surface of the moon fully faces the earth, making the moon appear round.
On a new moon phase, the moon is between the Sun and Earth. This means its light is not reflected to Earth. Instead, the light from the sun bounces back from the earth and causes a slight illumination on the moon.
All shapes or the phases of the moon indicate its position from the Sun and earth and how light behaves in relation to each.