Atmospheric Halos

These beautiful rainbows are caused by ice or water droplets floating in thin clouds above. These act like tiny prisms, and collectively they smear the sun's image into a plethora of arcs depending on the crystals and the position of the sun. The explanations for these arcs are nicely explained at Atmospheric Optics.

Ice Halos

These halos are caused by the ice crystals that form in clouds. Ice forms hexagonal prisms as a crystal, so the arcs created depend on the orientation of the prism.

Rainbows

Rainbows, unlike the majority of halos, are caused by water droplets instead of ice crystals. However, they are easily the most well-known of all the halos. This is probably because of its huge size and its location--away from the sun, it is easier to notice without burning your eyes out.