A Little Word On Japanese Mythology....
A note on the four worlds
According to Japanese mythology, their are four worlds: Reikai, the spirit world, a sort of Heaven, if you will, Ningenkai, the human world, Makai, the demon world and Meikai, which is essentially Hell.
The premise of the Yu Yu Hakusho story is that there are gateways or portals between these worlds, namely the Makai and Ningenkai and that there are detectives, reikai tantei, employed by the Reikai to stop unauthorized crossings between the worlds.
A word on demons
Unlike demons in western mythology, Japanese demons can be either good or evil depending on their mood. There are many different words for demons and each have seperate meanings and connotations, but, since the context I'm using is Yu Yu Hakusho, I will use the word youkai.
There are many different types of youkai, but I will only go into those mentioned in the series. Yusuke, descended from Raizen, is part Toushin.
Toushin, as far as I can tell, are humanoid and very agressive. They also have a nasty tendancy to eat people.
Kurama is a youko. Youko are mischevious, thieving fox demons, servants (theoretically) of Inari, the god of harvest. They have the ability to shift their shape from many-tailed foxes to something resembling a human man or woman with the ears, tail and eyes of a fox.
Hiei is a fire demon. That's...well, exactly what it sounds like, really. His power revolves around fire. Lastly, his sister Yukina is a koorime. Now, there are some people who say that since they're sibblings, Hiei must also be a koorime, but, since there are no male koorime, I find that a little hard to believe. The name koorime litterally means "ice maiden". They are a race of vampiric female demons who lure men into their icy domain to either feed on them or...ah...mate with them.
A note on Enma, Botan and the Sanzu no Kawa
Botan is like the Japanese equivalent of Charon. She ferries the souls of the dead across the Sanzu no Kawa, a sort of river Styx, on her flying oar. Botan brings the souls to the Hall of Judgement to stand before Enma-Daio, the king of the Reikai, a fierce giant. However, in the Yu Yu Hakusho story, it is the son of Enma-Daio, Ko-enma (Enma junior) who employs the Urameshi team. Their reasoning behind this is that since Enma-sama is so busy, he needs his son to help him process souls.