The moon appears to change sizes and shapes because its light is reflected sunlight which makes it appear the moon is glowing. We call the different sizes and shapes phases. There are 8 main phases of the moon cycle. The moon cycle takes about 29 days. The waxing phases are when the visible portion of the moon gets bigger. The waning phases are when the visible portion of the moon gets smaller.
A small slice of the moon is a crescent moon.
A mostly rounded shape (more than half illuminated) of the moon is a gibbous moon.
The gravitation pull of the moon on Earth causes tides. The oceans bulge in the direction of the moon and the direction opposite the moon. High tide is during the bulge, low tide is between the bulges of water.