The Hippogriff is a mythical monster that has the head, wings and fore-claws of an eagle and the hindquarters of a horse. Created in the Medieval period in monastic bestiaries, it was said to be the offspring of a griffon and a horse, hence the name (from "hippo", Greek for "horse", and "griff", for "griffon") - this made it a symbol of absolute impossibility, as lore in those same bestiaries portrayed griffons as absolutely hating horses. But, later generations didn't quite get the memo, and so hippogriffs have repeatedly appeared as real creatures in many fantasy settings, often with a deep mutual enmity for griffons.
You may wonder; just what is the point of a hippogriff, given it would have less combat power than a griffon due to lacking the raking rear claws? Well, in settings where they appear, hippogriffs tend to be faster and more agile than their griffon kindred, but also more readily domesticated. Griffons tend to be portrayed as either generally savage and unruly, or else only bonding to a single master after a long and oft-dangerous training period. Hippogriffs, in comparison, are more docile; they're easier to train, easier to control in battle, and generally less dangerous to friends than griffons.
In case you were morbidly curious; yes, they are a PC race in Ponyfinder, though it took until the "Griffons of Everglow" sourcebook for them to appear.