They are related to halos, but where halos are caused by a random diffusion of crystals before the light source and are circular, most arcs are formed by crystals whose orientation is specific and uniform and can take on many other shapes.

Why are there so many?
Given the different possible shapes of ice crystals (4 or so commonly in the cirrus layer), the range of lunar and solar elevations, the range of possible orientations of crystals in the sky, their uniformity and relative position to the source, as well as the discrete number of reflections off of and within the shape, there are a lot of possible permutations. Though this all sounds perfectly scientific, there are in fact some arcs that cannot yet be adequately explained, which means they still maintain some cosmic mystery.

Some of the more spectacular and/or common arcs are noded individually and are hardlinked. Others are described in brief below.

Needle crystal arcs

Diffuse arcs: Two white arcs that descend from the anthelion to the horizon like the bottom of an "X".
Ray path: sunlight passes into an edge face, reflecting off of three edge faces and the base plate before reflecting out the entrance face again. If the Earth was invisible, in simulation the diffuse arcs continue below the horizon to create a giant teardrop shape that evelopes the nadir, like an inverted Wegener anthelic arc.

Heliac arc: An extremely rare, faint white arc that forms an Ichthus in the sky.

Infralateral & Supralateral arcs: Colorful arcs that change dramatically with solar elevation.
Formation: Similarly oriented hexagonal needle-shaped ice crystals, solar elevation lower than 32°.
Ray path: Light either enters a base and exits an edge face.

Lowitz arcs: Discovered by Thomas Lowitz in 1794 in St. Petersburg, Lowitz arcs are short, faint rainbow-colroed arcs that connect parhelia to the 22° halo.
Formation: One theory says these are caused by plate-shaped crystals rotating along an axis that touches opposing points, rather than edges. A competing theory says these are just extensions of the lower Parry arc, which would mean it was a needle-shaped crystal in Parry orientation. They often occur in conjunction with plate-formed parhelia, so the former is probably more likely.

Parry arcs: Rare, white arcs that occur near the tangent arcs.

Tricker arc: The Tricker arc is a short loop that stretches about 5° above the anthelion.
Ray path: Light enters a base face, reflects off of two edge faces, the opposite base face, and then two more edge faces before passing out the entrance face again.

Wegener anthelic arc: Teardrop shape stretching between the anthelion and the upper tangent arc.

Sector plate crystal arcs

9° arcs: Rare, white sunvex arcs tangent to the 9° halo. There is one directly above and one directly below the sun. The lower arc cannot appear when the sun is above 50°.
Formation: singly oriented sector plate crystals whose long axis is nearly (20°) vertical. This almost never happens, so they often appear as brightenings of the 9° halo.
Ray path: Sunlight enters the small tip at the top of a pyramid and exits the tip of the opposite pyramid.

18° lateral arcs: When the 18° halo is visible, any of the four 18° sunvex lateral arcs may be visible as well, but may appear only as localized brightenings of the halo. They are kind of like 18° versions of tangent arcs and parhelia.
Formation: Vertically oriented sector crystals. (Sector plate crystals' "vertical" alignment is often tilted more than 10°.)
Ray path: Sunlight enters one pyramidal edge face and exits a face plate on the opposite hemisphere of the crystal, on the opposite side.

24° lateral arcs: Similar to the 18° arcs. When the 24° halo is visible, any of the four 24° sunvex lateral arcs may be visible as well, but may appear as localized brightenings of the halo.
Formation: Vertically oriented sector crystals. (Sector plate crystals' "vertical" alignment is often tilted more than 10°.)
Ray path: Sunlight enters one pyramidal edge face and exits a face plate on the same "hemisphere" of the crystal, but the opposite side.

Plate crystal arcs

Circumhorizontal arc: A gigantic, uncommon, brilliant, often suncave rainbow-colored arc that occurs at the horizon on the same side as the sun when the sun is high in the sky.

Circumzenith arc: A common, brilliant, often sunvex rainbow-colored arc directly overhead when the sun is low in the sky.

Arc (&?;), n. [F. arc, L. arcus bow, arc. See Arch, n.]

1. (Geom.)

A portion of a curved line; as, the arc of a circle or of an ellipse.

2.

A curvature in the shape of a circular arc or an arch; as, the colored arc (the rainbow); the arc of Hadley's quadrant.

3.

An arch. [Obs.]

Statues and trophies, and triumphal arcs.
Milton.

4.

The apparent arc described, above or below the horizon, by the sun or other celestial body. The diurnal arc is described during the daytime, the nocturnal arc during the night.

Electric arc, Voltaic arc. See under Voltaic.

© Webster 1913

Arc (ärk), v. i. [imp. & p. p. Arcked (ärkt); p. pr. & vb. n. Arcking.] (Elec.)

To form a voltaic arc, as an electrical current in a broken or disconnected circuit.

© Webster 1913