When the Aztecs traded and otherwise interacted culturally with the people there before them, they left behind more information than the Olmec stood themselves. In fact, it was the Aztecs who called the people Olmec to begin with. The term comes from a common resource in the area: rubber. Historians can only guess that it was one of the common trade goods that so impressed the Aztecs that they refer to the people in association with it.
No information exists to tell anyone what the Olmec called themselves. This civilization existed on the northern edge of Mesoamerica near the Gulf of Mexico. This area is now near the southern end of Mexico to the left of the Yucatán Peninsula. From a sociological perspective, it is an area that makes sense to settle in. The Gulf of Mexico offers a food source and the opportunity to travel more easily up and down the coast to trade with other civilizations.
Because the existence of the Olmec people occurred so long ago, it has proved quite difficult to establish some type of historical continuity to explain where they came from and why they disappeared over 1000 years later. By the time the years 400 to 300 BCE came around, no more evidence of this once-thriving group existed.
Despite the mystery surrounding their appearance and existence, the Olmec had considerable power in the region and quite a rich and cultured life. After all, in the nearly 2000 years they existed in the Mesoamerican region, they had time to establish trade routes, agriculture and ancient industry, plenty of artwork, and unique religious and cultural practices.