Note: All of the links in this answer point to various parts of Les Cowley's excellent Atmospheric Optics site. Les combines photographs, simulated images, and descriptions of the underlying physics to beautifully portray and explain a number of different optical effects in our atmosphere.
Note: The imagery on that site is copyrighted. Please do not edit this answer to portray images from that site.
That's a very nice picture that shows a number of ice halos. Ice crystal halos are caused by various shapes of ice crystals. Some of these halos such as the small circle that encircles the Sun in the image in the question are easily seen at all latitudes. Others only appear in very high latitudes, and even there they are rather infrequent.
The small circle is the 22° halo. This is a frequently seen halo, much more common than rainbows. It's caused by poorly aligned hexagonal prism ice crystals. If you look closely, you'll see that the sky is darker inside the 22° halo. This is similar to how the sky is darker outside the primary bow of a rainbow. Unlike a rainbow, the color separation is very small, making the 22° halo white rather than colored. If you look closely, you can see that the inner edge has a bit of a reddish tinge.
The two bright spots on the sides of the 22° halo are sun dogs. These result from hexagonal plates of ice with their large faces nearly horizontal. The curve the intersects the Sun, runs parallel to the horizon, and intersects the 22° halo at the sun dogs is the parhelic circle. Parhelic circles result from sunlight reflecting off nearly vertical faces of ice crystals. The mustache atop the 22° halo is the upper tangent arc. Tangent arcs result from ice crystals that form hexagonal columns rather than hexagonal plates. As is the case with the 22° halo, sun dogs, parhelic circles, and tangent arcs are fairly common.
The partial circle outside the 22° halo is the not so common supralateral arc, or possibly the even rarer 46° halo. Atop that is the circumzenithal arc.