 The Olmec were an ancient Pre-Columbian people living in south-central Mexico, in the modern-day states of Veracruz and Tabasco, from about 1200 BCE to 400 BCE.They are claimed by many to be the mother culture of every primary element common to later Mesoamerican civilizations.The name "Olmec" means "rubber people" in Nahuatl, the language of the Aztecs.