Atmospheric refraction, when the moon is nearly touching the horizon, changes the moon's shape, but this is not the reason either. It has the effect of making the moon look flatter, but not bigger.

What makes the moon appear larger is the comparison with distant surface objects like buildings and trees. The moon looks much bigger than them. When it's higher in the sky, it seems dwarfed by the vastness.

Each evening, the moon appears larger or smaller than the night before, depending on its phase. The full moon is coming up August 8 in the Western Hemisphere (August 9 in the Eastern) and that's when you'll notice the size phenomenon best.