You may have heard that the moon should appear the same size regardless of its position on the horizon, since its distance to the observer varies minimally with its position on the horizon. Therefore the fact that it appears larger when close to the horizon is an illusion.
What I did not know is that we don't fully understand the illusion. Three explanations are offered in this video.
One has to do with our brains performing a relative comparison with nearby objects of known size, such as trees, which is only possible when the moon appears on the horizon. But the explanation fails to account for the illusion also working for sailors and pilots, even though they don't have such objects to confuse them.
Another explanation involves perspective correction, where things that are far away are assumed to be bigger. The video has a nice illustration of this.
Yet a third explanation is that the brain judges distance by taking into account how much our eyes need to focus to observe something. This focus is different for the horizon and for looking at the top of the sky.
No single explanation works in all cases, so amazingly we still don't know why the moon appears larger. Check out the video for a more visual explanation of the same points.
And here is wikipedia’s take.