Sun dogs, or parhelia, are little back-up suns that appear on either side of the sun. They are the Pips to the sun's Gladys, the Lion and the Witch to the sun's Wardrobe, and they look way cooler than rainbows.
What is it that makes these parhelia possible? Only the most badass shape in the whole world: the hexagon. It's the geometric shape that rhymes with sex and means ‘an evil spell.' It's balanced, edgy. It's got an angle on everything. It's what the pentagon would have been if the government hadn't been too cheap to add that last wall. There's nothing that the hexagon can't do. When it gets cold enough, hexagons fall from the sky. Literally.
When water freezes it forms hexagonal crystals. Sometimes the crystals are long, pencil-shaped objects, but much of the time they are flat disks. When they fall, the flat side turns parallel to the earth, due to Io9's old friend, the Bernoulli Effect. When the disk tilts so that an edge pushes out, the air around it rushes past faster. This creates a low pressure zone and pulls the crystal's edges out harder, until it is flat-side-down.
This leaves the hexagonal shape of the crystal open to exploitation by miscreant sun beams. Most of us know that certain substances, including ice, can bend light. It's difficult to understand, though, how this would make duplicate suns appear.
Picture someone looking at a regular sunset. It's pretty easy to understand the course of the light. The sun gives off photons in all directions, and some of them travel in a straight line until they hit the the person's eyeball, allowing them to see the image of the sun. Now picture two other people on either side of the original person, about a quarter mile away. They would also get face-fulls of photons, allowing them to see the sun.
The same thing would happen during a cold sunset with ice crystals in the air. Some of the photons would travel in a straight line and hit each person's eyeball letting them see the sun. But they wouldn't get an eyeful all the photons which had originally travelled in that direction. Because of the hexagonal crystals in the air, some of the photons - part of the image of what the two other people would see – would be caught and redirected to the original person's position. They would see images of the sun not just from straight ahead of them, but coming in from either side.
Since the images would be coming from either side of the sun, and we assume from experience that light travels in straight lines, the person would think they were seeing three suns next to each other in the sky.