The Moon appears to change shape because we see different amounts of the lit part as the Moon orbits Earth. When the Moon is between Earth and the Sun, the lit side is hidden from us. As it moves around Earth, more and more of the lit side comes into view. Then it begins to disappear again.
The amount of Moon we see changes over the month — lunar phases — because the Moon orbits Earth and Earth orbits the Sun. Everything is moving. During a lunar eclipse, Earth comes between the Sun and the Moon, blocking the sunlight falling on the Moon. Earth's shadow covers all or part of the lunar surface.
"When the moon is near the horizon, the ground and horizon make the moon appear relatively close. Because the moon is changing its apparent position in depth while the light stimulus remains constant, the brain's size-distance mechanism changes its perceived size and makes the moon appear very large.
The Moon illusion is the name for this trick our brains play on us. Photographs prove that the Moon is the same width near the horizon as when it's high in the sky, but that's not what we perceive with our eyes. Thus it's an illusion rooted in the way our brains process visual information.