A sundog is a bright patch in the sky that you can sometimes see, about as big as the Sun itself, and at the same height above the horizon as the Sun, but about 20 degrees (two fist-widths at arm's length) to the left or to the right of the Sun. Sundogs are usually reddish on the side nearest the Sun, white in the center, and bluish on the side farthest from the Sun. A sundog is made of light from the Sun that is reflected off of very tiny ice crystals in the air. Sundogs are related to rainbows and halos. (A halo is a ring around the Sun or Moon.)
Where sundogs come from
When you go up into the air it gets very cold, below freezing. High clouds are in freezing air and they are made of ice crystals that are so small you can't even see them one by one. Sometimes those clouds are so thin that you can look right through them. Sometimes they make the sky look milky. These ice crystals often look like hexagonal prisms. A hexagonal prism is kind of like a glass that is not round but rather has six sides on the outside (not counting the bottom) and that is filled to the brim with glass, too. When you rotate such a prism (or a six-sided glass filled to the top with water) near a lamp then you see reflections of the lamp off of the sides of the glass and through the glass, but only if you hold the glass in just the right way. The same thing happens to sunlight when it hits those ice crystals in the sky.
In some clouds of ice crystals the crystals all line up vertically so that their "top" is really at the top and the "bottom" really at the bottom, and the six other sides are vertical like a door. In that case we only see the reflected light when it comes from ice crystals that appear to be as high in the sky as the Sun itself is. Because of the six-sided shape of the crystals and because of the material (water ice) that they are made of, the reflection off of the ice crystals works best for ice crystals that are about 22 degrees away from the Sun. If you stretch out your arm and look at your closed fist (palm forward) then your fist is about 10 degrees wide, so in this way you should be able to fit your fist twice between the Sun (or Moon) and the sundog.
There are only two places in the sky that appear as high as the Sun itself and that are about 22 degrees away from the Sun: about two fists to the left of the Sun and about two fists to the right of the Sun, and that's where you can see sundogs.
So, a sundog is made of light from the Sun that is reflected off of tiny ice crystals in the sky that are all lined up vertically. A sundog is always as high in the sky as the Sun itself, and they are always at about the same distance from the Sun. If you see a sundog, then there are lined-up ice crystals in that direction. A sundog disappears when the cloud of ice crystals moves away from the sundog-point in the sky, or if the cloud gets so thick over there that the sunlight cannot get through anymore, or if the cloud gets so thin that there are too few ice crystals to reflect off of, or if the ice crystals do not line up anymore, or if the Sun sets.
