Inbreeding is the mating among members of a family. It is an instrument in all livestock breeding to solidify traits, i.e. to firmly install them genetically. Usually, if the inbreeding is not too close, it is referred to as "linebreeding" (for instance uncle x niece, grandsire x granddaughter). Another definition known among horse breeders is the saying: "If it works, it's linebreeding, if it doesn't, it's inbreeding." Sire x daughter or son x dam, or brother x sister is so close that it is inbreeding and can't be considered linebreeding.
While linebreeding is used to genetically secure positive traits in a breed and to achieve uniformity, it can backfire, as negative traits might be made worst. Intensive inbreeding is a sure way to degenerate and ruin a population. Lack of vigour, soundness, and fertility as well as conformation defects are the most common problems.
The Sorraia horse has survived extreme inbreeding, and extreme close inbreeding, for many generations, and the fact that these horses are still sound and fertile is a miracle, but can also be viewed as evidence for its primitive origin. Arguably, no man-made breed could have survived such extreme inbreeding, and even the Mongolian wild horse, which, like the Sorraia, goes back to just a handful of founding horses, has suffered much more in reduced fertility than the Sorraia.