Generation is the trait that indicates how far down a horse is from the beginning of its family tree.
The O1 generation of racehorses are the rarest, and have the highest performance potential. The higher the horse's generation number (the further it is from O1), the lower its likelihood of having strong racing ability.
O1 generation racehorses cannot be reproduced. When two O1 horses are bred, they produce a O2 horse, which is the highest generation that can be produced through breeding.