Demons come from Hell. Instead of blood, demons seem to have white snakes inside their bodies that flee out of them when the demon's flesh is cut. Losing too much of those white snakes can cause vital problems for the demon.
They all seem to be following some kind of plan which presumably leads to the Apocalypse and End of Days for mankind. Little has been revealed of that plan yet, but it includes using the Department of Integration to increase the creature-to-human ratio, diminishing the human population in the progress.
The only ones who are able to stop the Apocalypse are the wizards, which is why the demons lead a war against them, as seen in "Wet Hot Demonic Summer".
The demons, together with the humans and zombies of New York City, regularly act out an extremely realistic and brutal End of Days War Pre-Enactment which involves false guns, gory special effects and false nukes. The zombies seem to be allies with the demons in these scenarios.
Many demons have been shown to take on at least two different forms. They mostly appear in their human-like forms but can change to a more intimidating, bigger form with wings, claws and a tail that is closer to classic depictions of demons. Callie is also shown to shapeshift into a human.
Demons have very unique mating habits that may appear strange and brutal to outsiders. It seems that the natural demon mating ritual actually diminishes the demon population, considering that, as part of the ritual, the male not only slaughters his rival, but also kills the female demon and devours the baby. Thus, demons must be created in so-called Baby Factories in "Old Hell".
Demons have a Zechalech ceremony which is a celebration for female demons. A part of this ceremony includes a participating female demon obtaining a soul from a human man.