wife of Pirithoüs (a son of Zeus), and the daughter of Oenomaüs who became the wife of Pelops.
It means 'horse tamer' from hippos, 'horse' and damao, 'to tame', and as a favourable name really means 'one who is high-born', 'one who owns many horses'. (Significantly, even today, in a different era and a different culture, the prestige of owning and riding a horse is still considerable, not least for a woman.) One should not overlook the 'taming' aspect of the name, either, which relates to the mastery of horses and chariots. (A goddess so named could give a person the power to tame horses.)
There is a specific connection for Hippodamia the wife of Pelops, since she married her husband as the result of a 'rigged' chariot race which he won - and thus qualified to carry her off. Jane Harrison sees this story evolving from actual races which took place in the original Olympic games; in these, young men raced in chariots and girls (virgins) raced on foot.