The Moon illusion is an optical illusion which causes the Moon to appear larger near the horizon than it does higher up in the sky. It has been known since ancient times and recorded by various cultures. The explanation of this illusion is still debated."

Source : Wikipedia

What is known is that it's a purely psychological illusion rather than an optical one. The same phenomenon causes distant hills to look far more steeply inclined than they actually are.

Further reading: Helen Ross; Cornelis Plug (2002) The Mystery of The Moon Illusion.^{[ paywalled ]} USA: Oxford University Press.

Editor's Note:

For those not convinced that it's a purely psychological illusion, try the the following experiment : When the Moon is low, and looks particularly large, find a very small coin (or other disc) that is exactly the right size to obscure the Moon when held at arm's length. On a subsequent evening, when the Moon is high, and appears small, take the same coin, at the same arm's length, and it will perfectly fit the Moon, as before.

For a 'live' demonstration of the peculiarity of the illusion, hold up a small coin as in the example above, and then focus your eye on the coin itself - whilst paying close attention to the apparent 'size' of the Moon. You should see the Moon appear to 'shrink' as you do so. Focus on the Moon again, and it will 'grow' back to its enlarged size.