Since the moon orbits earth, we see it from different angles. The phases of the moon are our changing views of light on the moon. The phase of the moon begins when it moves between earth and the sun. Remember that the moon does not have its own light, it shines because it reflects the light received from the sun.
Every month, there are four main lunar phases: New Moon, First Quarter Moon, Full Moon and Last Quarter Moon. The New Moon is when the bright side of the Moon is facing away from us, and we see the dark near side.
Since the Moon is constantly moving along its orbit, it changes shape every night. Started from the New Moon phase, we see more of the near side side lit up until the phase of Full Moon. Once it reaches the Full Moon phase, the moon is waning/decreasing, and we will see less and less of the moon lit up until it disappears at the next New Moon. The cycle can actually be divided even further into eight obvious stages.

New Moon - First/Waxing Crescent - First Quarter- Waxing Gibbous Moon - Full Moon - Waning Gibbous - Last Quarter - Waning Crescent - the next New Moon