Clouds Behind the Moon

So it's very early Thursday morning, still dark here.  Wednesday was rainy, with some sun breaks, then rainy again.  But in the past several hours it's cleared enough to see a few stars among the clouds, and especially a super-bright not quite full Moon.

It was so bright that I went outside to check it out.  Moonlight on the cala lillies.  Towards the western horizon, the very bright disc looking especially three-dimensional as the clouds passed behind it.

Wait a minute--behind it?  Yes.  The pretty substantial looking clouds were moving horizontally behind the moon.  Although it's freezing out there, I took a real good look.  And then came back in to google it.

Turns out it is not an unknown sight.  There are youtube vids and photos, like this one.  Googling was less interesting than ogling, though.  In answer to the question, how can clouds be moving behind the moon, most of the answers were brief and elementary, with the tone of an adult explaining something to an idiot child: the clouds can't be behind the moon because the clouds are only a few miles up and the moon is like a million miles away.  The clouds are on Earth, the Moon is the Moon, see? 

Welll you know I figured that out myself.  What I wondered is what accounts for the optical illusion?  I'll bet that might be interesting.  It was a remarkable sight anyway.