Why do we see the Moon change throughout the month?

The Moon is a sphere which travels once around the Earth every 29.5 days. As it does so, it is illuminated from varying angles by the Sun. At New Moon, the Moon is between the Earth and Sun, so that the side of the Moon facing towards us receives no direct sunlight, and is only lit by dim sunlight reflected from the Earth. As it moves around the Earth, the side we can see gradually becomes more illuminated by direct sunlight.

After a week, the Moon is 90° away from the Sun in the sky and is half illuminated, what we call First Quarter because it is about a quarter of the way around the Earth.

A week after this, the Moon is 180° away from the Sun, so that Sun, Earth and Moon form a line. The Moon is fully illuminated by the Sun, so this is called Full Moon. The Earth's shadow points towards the Moon at this time, but usually the Moon passes above or below the shadow and no eclipse occurs.

A week later the Moon has moved another quarter of the way around the Earth, to the Third Quarter position. The Sun's light is now shining on the other half of the visible face of the Moon.

Finally, a week later, the Moon is back to its New Moon starting position. Usually it passes above or below the Sun, but occasionally it passes right in front of the Sun, and we get an eclipse of the Sun.

The Moon's phases are NOT caused by the shadow of the Earth falling on the Moon. In fact the shadow of the Earth only falls on the Moon for a few hours twice a year when there is a lunar eclipse.

We could see moon only in presence of light given by sun. So the part it gets light from sun luminous object we could only see that much.