The moon does not shine on its own, but it instead reflects light from the sun. However, it only reflects a small fraction of light, so humans don't see the moon as brightly they do the sun. This makes it safe to look at it without requiring eye protection.
The moon revolves around Earth once per month and follows an elliptical orbit. Therefore, its distance and orientation vary, which is why the moon sometimes looks larger than other times. The same side of the moon is always facing the Earth because its rotation period matches its orbit around Earth.
Humans only see half of the moon from Earth at any given point during the month. Depending on where it is in relation to the sun, it looks different to observers. For example, the new moon occurs when the moon is between the sun and Earth, so humans see no reflected sunlight. Gradually, the moon begins to appear as a crescent, as a semicircle and as the full moon when sunlight reflects fully off the part visible from Earth. The full moon gradually wanes until the new moon is in the sky again at the start of the next lunar cycle.