"Possession demons" are demons found on Earth, so called because they typically possess mortals to travel incognito. (The term does not actually appear in the comic.) They are spiritual entities and are not typically able to free themselves from a mortal vessel. They are approximately the size of a shoulder angel or devil, if they can be said to have a size at all.
While their mortal vessels can change shape and exhibit certain demonic traits, these demons usually keep a normal physical form. However, their vessels act oddly, appearing silent and withdrawn, even if two demons are chatting or confronting each other on a mental level. Possession demons do not recognize each other except by initiating mental contact or showing a demonic trait.
As shown by the example of K'Z'K, possessing mortals is at least sometimes a temporary role a demon adopts rather than part of its nature or its usual method of operating. On the other hand, those demons appearing as possessors do seem to require a host. In some cases this is explained by the way the demons have entered the world in the first place. K'Z'K possessed Gwynn first before he was freed from the Book of E-Ville and later when he was nothing but a sentient fragment of himself attached to her soul (and only in the latter case acted as possession demons usually do); Skippy was apparently accidentally summoned straight into his host rather than into the external world.
While all the possession demons we have seen revere K'Z'K and seek to bring about the end of the world, a division has arisen in their ranks about how best to do that. The demons that follow Skippy believe only K'Z'K can bring about The End, while the ones that follow Chilus (the Cult of K'Z'K) believe that they can end the world without him.
There are numerous prophecies relevant to the demons' goal. One of the important figures in those prophecies is the Storm Breaker, Zoë. She has already destroyed K'Z'K once, but may have a further role to play.