Foundation horses have pedigrees that trace strongly back to the founding horses of a breed. Horse breeds evolve as people breed them for different purposes, meaning that purebred horses of today may no longer resemble the founding horses of the breed. For example, quarter horses today may be registered as AQHA but really be as little as 10% foundation blood, and may even be part Thoroughbred. If you look at the original 'bull dog' foundation quarter horses-- small, strong, short-legged and well muscled-- they look nothing like the tall, slender show horses seen in some AQHA shows. The breed evolves as people breed for different events; Although two horses may be purebred QH, a barrel horse looks and moves far differently than a western pleasure horse.

There is a quarter horse foundation registry that will certify horses having a certain percentage of foundation blood; horses may be 80% foundation or more in order to be registered with the NFQHA (National Foundation Quarter Horse Associaiton).
If you see a horse advertised as a foundation mare or stallion, this probably means that the horse contains a high percentage of foundation bloodlines and is registered or certified in their breed's foundation association.