Spotted out the plane window over western Arkansas. Well, I said I was going to do more science posts, so why not start with this thing?
It's called a glory because it looks like the archetypal halo around the head of a saint. You see them directly opposite the Sun (so always below the horizon) in clouds of uniformly-sized drops of water. The exact formation mechanism is not known, but we have clues. The light in the center is polarized, so there must be at least one reflection inside the droplet, as well as two refractions (entering the drop and leaving the drop). And obviously, since we see them opposite the sun, the light must be bent around 180º (light going away from the Sun has to be turned completely around to come back to your eye). More sophisticated analysis shows most of the brightness is due to one reflection inside the water drop.
But it's not possible to turn the light 180º! At least, not with only one reflection and two refractions! So the explanation is that the light travels briefly along the surface of the drop as a surface wave. A diagram, and more explanation, can be found here.
A light ray enters one side of a drop and comes out the other side. A different ray enters where the first exits, and exits where the first enters. They interfere with each other, which causes the colored rings.
So the glory occurs directly opposite the Sun, which is the place where your shadow is. Therefore, your shadow will appear right in the center. In the top photo, you can tell I was sitting in the back of the plane. Like rainbows, glories aren't located at a physical place in space - every person sees a different glory. So if you and I were standing side by side looking at a glory, I would see the shadow of my head in the middle and yours off to the side, and you would see the shadow of your head in the middle and mine off to the side. Everyone sees their own glory, and no one else's.
That's the 'natural' picture of it - well, through a nasty, low-contrast aircraft window, anyways. I can make it easier to see by cranking the global contrast way up. The color has not been adjusted:
Now you can clearly see the structure: Bright in the middle with colored rings outside.
Things which you'd never notice unless you knew to look.