The difference between "waxing" and "waning" is the same as between "increasing" and "decreasing." When something is waxing, it is getting closer to its maximum property. When something is waning, it is decreasing, or getting closer to its minimum property.
"Waxing" and "waning" are used to describe the phases of the moon. When the moon is waxing, it is going from the new moon to the full moon, or from between the Earth and sun to behind the Earth. During this journey, the crescent of the moon is losing darkness and gaining light. When the moon is waning, the reverse is happening until it reaches the completely dark, new moon.