Half-demons are what they sound like: they have a demon parent and a human parent. Often, the human parent will be an exorcist, as only people who have recieved a Temptaint, also called Mashou, can see demons.
Half-demons' appearance can vary heavily based on who their parents are, but they typically have pointed ears and a tail. A few have cat-slit pupils.
Again, half-demons' abilities vary greatly and depend on who their parents are, but most of them have very quick healing and regenerative abilities and inhuman strength, speed, and stamina.