Good day, student of introductory astronomy!

Since you were interested enough to inquire, I will pass along the following to you. This is in regards to the question of the apparent size of the Moon as it appears in the sky.

Caption: Moonrise over Seattle. Credit Shay Stephens.

The first effect is a real one. The angular diameter of the Moon is proportional to the ratio of the Moon's physical diameter (3476 km) to its distance from Earth (about 384,400 km from the Earth's center on average). Using the small angle approximation, this angular diameter as measured from the center of the Earth works out to be about 0.518 degrees (31.1 arc minutes; a small correction would be needed to account for the fact that the observer lies somewhere on the Earth's surface). However, the Moon's center may be as far away as 406,600 km and as near as 356,600 km from the Earth's center1. These angular diameters are 0.490 degrees (29.4 arc minutes) and 0.558 degrees (33.5 arc minutes), as measured there. This difference in angular diameter of roughly 4.1 arc minutes (about 13% of the Moon's average angular size) is noticable to the human eye. So some full moons appear larger because they span a larger angular diameter in the sky (the Moon happens to lie closer to the Earth).

Caption: courtesy of the Earth Science Picture of the Day; distances and angular diameters are measured at the observer rather than at the center of the Earth. Originating website can be found here.

But there is more to this phenomenon of the apparent Moon size than that...

The second effect is an illusionary one. For a variety of reasons having to do with how the human eye and brain work together, the human brain interprets a full moon lying near the horizon to appear larger than when it lies high in the sky, away from the horizon. You can test for yourself that the Moon's angular diameter is exactly the same near the horizon as it is when it is up high in the sky, by holding an object at arm's length whose angular size matches that of the moon (see also the top photo). You can go here, here, here, and here for further information about this illusion - the psycho-physiological explanations are still controversial! NASA has a webpage providing a nice summary of the problem and several links for more information. The same illusion applies to a rising or setting Sun.

Now sometimes these effects can work together to produce a "really big Moon" as it lies near the horizon. A rising (or setting) full Moon that lies at perigee (its closest approach to Earth) will indeed appear to loom extra large along the horizon. Part of the effect is real, part is an illusion.