The Shivarra, or Shivan, are a 6-armed female mystical demonspecies living in Outland, averaging at roughly twenty to thirty feet tall. Currently, not much is known about these dangerous demons except the small excerpt of information stored on the Exodar Holographic Emitter in the Exodar.
Shivarra serve the Burning Legion as priestesses and military chaplains. They are devout and charismatic and as such are a driving force behind the Burning Legion as all their efforts are bent on bringing Sargeras' vision into being.
Shivan appears to be another term used for these mystical demons living in Outland, also called the shivarra race. So far the only known example of a shivan are Shivan Assassins. It has been theorized that "shivarra" is the draenei term, while "shivan" is a more common name. Alternatively, "shivan" could be the adjective form of "shivarra." A third notion is that the shivan are a species of the shivarra.
The shivarra are inspired, in both form and name, by a number of Hindu deities, the Devas. Devas tend to have multiple arms, and unlike the shivarra, are almost always good-aligned. The name "shivarra" is likely taken from Shiva the Destroyer, one of the three most powerful Hindu gods. The personality and specific appearance of the shivarra was probably inspired by Durga and Kali, forms of Shiva's consort, Devi.
It appears that the name changed prior to release from "shivan" to "shivarra," presumably to avoid the direct Hinduistic reference, though shivan still appears in-game.
As with harpies and sayaad, no information exists (in World of Warcraft) on males of the species.