Hippogriffs, although stunningly beautiful, have a reputation for being quite dangerous. They are proud and noble creatures. They demand to be regarded with due respect and are easily offended. It would be a big mistake to insult a Hippogriff. They have the body, tail and back legs of a horse, and the wings, head and front legs of a giant eagle. Hippogriff coats can be many colors including stormy gray, bronze, pinkish roan, gleaming chestnut, and inky black. To approach a Hippogriff one should first bow his head and then wait for the Hippogriff to bow back. 
Named Hippogriffs include Buckbeak, who is was also know as "Witherwings" after being put back in Hagrid's care after Sirius' death.
Hippogriffs are featured in the third book.
In the Goblet of fire Sirius meets the trio in Hogsmaede, disguised as the "dog form-animagus". He then leads them to a cave in which Buckbeak is hiding. And they have a conversation about Harry's participation in the Tri-Wizard Tournament while Buckbeak is being fed by Sirius.
Buckbeak also has a part in the Order of the Phoenix. Kreacher injures Buckbeak in order for Sirius to stay away from the fireplace so Harry cannot make contact with him. This is the trigger-point for Harry to go to Sirius's aid.
In the Half-Blood Prince, Dumbledore explains to Harry that Harry himself is now owner of Buckbeak, through Sirius's will and testament. But for the time being Buckbeak is staying at Hagrid's place so they had to rename him in order for the ministry not to get wind of the sentenced Hippogriff being at Hagrid's.