The moon is usually the same average distance from us (about 380,000 km) and while this distance can vary over the course of a year or a decade, the change in moon's size isn't easily detectable. The moon's orbit is elliptical, so at certain times it is closer and will appear bigger, but Sam is referring to the fact that the moon can appear different sizes on the same night, particularly when it's lower down in the sky. It's called "The Moon Illusion" and a huge number of Scientists have written about it including Aristotle, Thomas Young and Ibn Al Haytham (the co-inventor of Science itself).
The first thing to rule out is optical phenomena. If you compare photographs of the moon at different points in the sky, you can show that the moon's size is always the same in the camera lens. There is no distortion of light caused by the atmosphere. This means the effect is taking place inside our brains, rather than in the actual sky itself. It's an optical illusion and straight away that means things will get foggy.
The cause for this illusion is difficult to pin down, but the same is true for all illusions. Because we still have no idea how the brain percieves reality and how vision works, any question about perception will always come with a bit of hand-wavy ifs and maybes. The short version is that really bad at judging the world and analysing it. That's one of the reasons we invented Science, to get around the fact that our senses basically suck.
For some reason, when we look at the moon near the horizon we mistake it for bigger. The explanation may be something along the following lines: we see it in the sky on its own and get a sense of how big it is. When we see it near the horizon we expect it to appear smaller by comparison. Yet, it refuses to be any smaller. Our brain is confused: the moon is now next to an enormous horizon, so it should appear less significant, yet it doesn't. Ah, says the brain, I know what's going on - the moon must be bigger! And thus our brain sees the moon as it really is but convinces our conscious interpretation that it has somehow swelled in size. Moral of the story: your brain is not always your ally.