Centaurs are very mysterious creatures. They watch and read the signs in the stars and planets and they do not take sides in the events unfolding around them, which they have foreseen.
Centaurs avoid Muggles and wizards alike (FB). A number of centaurs live in the Forbidden Forest, including Ronan (PS15), Bane (PS15), Magorian (OP30) and up until Harry's fifth year, Firenze (PS15, OP27). They prefer simply to observe events they have predicted instead of taking part in them (PS15). The centaurs have chosen to be considered Beasts by theMinistry (FB) and do not take part in governing at all..
Centaurs figure in Greek mythology. In many cases, Centaurs represent animalistic behaviour – carrying off human women, for example – but they also appear as wise teachers. The Centaurs in the Harry Potter books demonstrate both traits. Bane carries off Umbridge when she insults and attacks the herd. Firenze, on the other hand, becomes a teacher at Hogwarts, even though he is banished from the herd because of associating with wizards (The Lexiconpage 55).
This creature was not invented by J.K. Rowling.