|“||It was a terrible, indescribable thing vaster than any subway train—a shapeless congeries of protoplasmic bubbles, faintly self-luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter.||„|
|~ A description of a Shoggoth|
Howard Phillips Lovecraft was a horror writer who influenced the genre greatly. Instead of traditional villains, he created "horrors": indescribable, indefinable, inconceivable beings, whose existence contradicts the laws of physics, whose aspect alone is beyond human logic, and as such can induce madness by their mere presence. Although malevolent by human standards, most of Lovecraft's "horrors" are amoral beings that are either insane or too alien for humans to understand. Very few of them are desirable to be around, however, and thus are similiar to villains in the sense of being harmful, and generally a threat to the world at large.
The term "Lovecraftian Horrors", also known as Eldritch Abominations, applies to villains who are or eventually transform into otherworldly entities beyond rationalisation, too alien from "normal" flesh-and-blood beings to be described properly, and most often madness-inducing. Alternatively, beings whose aspect is clearly stated to be an approximation of what they really are, something that humans can process while their real form is unconceivable. At the very least they must be as close as possible to such beings and a clear, stated tribute to Lovecraft.
HIGHLY IMPORTANT: No matter how nightmarish, villains who are merely gigantic and hideous and/or an amalgation of creatures do NOT fit in this category. Cosmic Entities and Energy Beings can (and frequently do) overlap with Lovecraftian Horrors, but are distinct types of villains.