The apparent phases of the moon correspond to how much of its sunlit surface can be seen by earth. The amount of the moon's sunlit surface visible from earth is greater when the moon is far apart from the sun in our sky, and less when the moon is close to the sun in the sky. In other words, when the moon is full, it is opposite the sun in the sky. When the moon is new, it is with the sun in the sky. That's enough variation to make the moon noticeably larger when closer to us.
Many people believe the moon is larger when seen at their horizon.
The full cycle of lunar phases, the time between successive full moons, defines a Synodic Month and is 29.5 days long. Historically this is what humans have meant by a 'month'. Because of the combination of the moon's orbit around earth and earth's orbit around the sun, it takes less time for the moon to return to the same position in space, measured relative to the stars. This month of 27.3 days is called a Sidereal Month . The picture below is a simple representation of the moon's orbit around the earth.