A parhelic circle is a white circle of light which appears at the same elevation like the sun and goes round the sky parallel to the horizon. It is called the parhelic circle because the parhelia are positioned on it. A parhelic circle is a reflection halo, so that it has the same colour like the sun. A complete parhelic circle is visible at very few occasions because to generate a complete parhelic circle, the ice crystals have to cover a great part of the sky.
A parhelic circle is normally caused by reflection of sunlight from the vertically orientated faces of ice crystals. Plate-shaped crystals reflect the sunlight from their prism faces, while column-shaped crystals reflect the light from their base faces. But there are many other light paths possible. Here is one example: In plate-shaped crystals the light is reflected internally by one of the prism faces. The light enters the upper base face, gets reflected from the inner side of a prism face and leaves the lower base face. The refractions at the points where the light enters and leaves the crystal neutralize one another, so that the light doesn't get divided into its colours.