Of course, demonology is the study of demons and their activity -- that's the easy, straightforward part. The not-so-easy part is understanding what all it entails. Most people in western culture are familiar with the Catholic notion of demonology and demonic activity. Demons are non-human spirits that are followers of Satan and seek to destroy mankind by leading people into temptation. All kinds of hideous acts have been blamed on demonic possession, and many people have said that they were attacked by demons trying to inhabit their body, receiving scratches and other physical wounds as a result. I've spoken with people who have experienced such phenomena, but never have I been on the receiving end.
I should mention that demonology varies incredibly from culture to culture. Some have beliefs that are at least somewhat aligned with the Catholic view on demons, while others believe that demons (or daemons, as they call them) are actually spirits just under the gods. Jin, or Genies, have been described by some as demonic, although there are many in Arabic cultures who disagree with this assessment.
My personal favorite daemon in fiction is Sauron from Middle Earth.
Have you ever experienced activity you believe to be demonic?