Omegaverse fic is a sub-genre of fanfic that became popular in the fandom from mid-2010 onwards, and is now found in many fandoms. The genre overlays canine-type characteristics on people, including pack hierarchies, the idea that receptive sex partners may go into heat and the canine characteristics of penis' having a bulbous knot at its base. The genre is also referred to as A/B/O fic after the Alpha/Beta/Omega divisions of pack hierarchies.
There is no single accepted set of 'rules' for stories written in the genre, but they usually includes strong themes of dominance and submission, and possessiveness. Most stories focus on Alphas bonding and mating with Omegas, and there is a strong use of the "soul mate" trope as well as the concept of sex (or mating) as a biological imperative. Some stories will build alternate societal and cultural traditions, while others insert the Omegaverse conventions into an otherwise 'real world' or canonical story story.
Alphas are almost exclusively Tops. Alphas may experience a "rutting" period which is analogous to going into heat. As mentioned, fic in this genre features the presence of a anatomical feature at the base of the penis that forms a knot when erect, as is found in dogs and wolves. See Knotting for more details.
Omegas may experience anal lubrication during heat, and sometimes spontaneous lactation. They may also have a very small penis. Mpreg is a common theme, with multiple births (as in a litter) common.
While some fics explore the idea of fluidity between Alphas, Beta and Omega states, they are in general defined in a rather rigid essentialist way.