Final answer:
The term that represents the increasing amount of light seen on the surface of the Moon is waxing. Waxing refers to the interval when the Moon grows fuller after the new moon and before the full moon, including the waxing gibbous phase.
Step-by-step explanation:
The term that represents the growing or increasing amount of light seen on the surface of the Moon is waxing. As the Moon transitions from the first quarter phase to a full moon, we observe more of its illuminated hemisphere, an interval known as the waxing gibbous phase. After a full moon, when the illuminated portion decreases, it is referred to as waning. The word gibbous is used when more than half of the Moon is illuminated but it's not yet full, while the term crescent relates to when less than half is illuminated.
The monthly cycle of the Moon, lasting about 29.5 days, showcases this fascinating transition from a new moon, to a crescent, to the gibbous form, and eventually to the full moon, before the cycle reverses. This cadence gave rise to the word 'month', which has its roots linked to the word 'moon'. The changing appearance of the Moon, though perceived as an illusion, is due to the interplay of sunlight and the Moon's orbit around Earth.