Snake Demon is the term applied to the three highest-ranking Demon Princes of Hell.
Before the First Battle there were other Demons of the same rank who did not escape the banishment to the Void, or fled elsewhere other than to the Demonic Planes (such as the Kurakil). During the First Battle the demons of this rank acted as Field Generals of the forces of Evil ranking alongside the likes of Arhallogen and Voivod.
There are three such Snake Demons named Ishtra, Myurr and Sith. They are inhumanly cruel to all of their servants but this pales into insignificance compared to their cruelty to Humans. They answer only to the Dark Lords. Far from being co-operative with one another in their constant struggle for domination of the world they actually fight with one another constantly.
It should be noted that these Demons might take many forms. The reason these Demons are called Snake Demons by scholars is due to Sith's passion for Snakes. It is she who is commonly referred to in the form of a Snake. The forms that Ishtra and Myurr take are often very different but the term Snake Demon has stuck.