That is a complicated question and to answer it in a way that is more illuminating to the readers out there who do not know much about the Olmec, I am going to address it and some broader Mesoamerican history at the same time. If you don't want this contextual information, just skip to my second reply below.

Before we begin, I should offer two disclaimers - I do not specialize in the study of the Olmec and more importantly that field remains very divided due to the limited amount of archaeological data we have on the Olmec and the extent to which much of our current understanding of the Olmec relies on extensive interpretation of that limited dataset.

Neverthless the archaeological data we do have suggests that the rise of the Olmec civilization proper during the Early Formative (~1000 BCE) coincided with a significant increase in regional trade ties across much of Mesoamerica. Readers who are unfamiliar with Mesoamerican history should know that Mesoamerican culture was in its infancy during this timeframe and that this development was one of the seminal moments in the overall evolution of Mesoamerica. While the nature of depositional means that only certain kinds of artifacts will be preserved in the archaeological record for an extended period of time, Archaeologists are fairly certain that ritual goods and precious stones were among the primary goods being exchanged by Mesoamericans in this first example of a pan-Mesoamerican trade network. Trade goods identified as originating in the Olmec heartland as well Olmec-inspired iconography found at distant sites like Tlatilco and Chalcatzingo point to the centrality of the Olmec to this activity, which raises several questions about early Mesoamerican trade: what allowed the Olmec to take such a preeminent role in this trade activity? What does the widespread dispersal of Olmec religious paraphernalia across Mesoamerica say about the nature of this exchange?

To answer these questions we must consider several factors. Even during this early time period, Mesoamerica was a very culturally diverse region. When one considers the difficulty of facilitating trade across a wide range of cultural and linguistic barriers (to say nothing of the complicated logistics of moving goods over long distances) it becomes apparent that the growth of this trade network must have reflected a profound shift in the nature of Mesoamerican affairs. Archaeologists generally agree that, save for a few notable sites, most Mesoamerican societies during this time frame exhibited a limited amount of social complexity. While burial deposits and site layouts do point to a degree of social stratification, most Mesoamerican societies do not appear to have the complex social hierarchies and individual specialization that is associated with "civilization". Monumental architecture as Olmec sites like San Lorenzo Tenochtitlan, La Venta, and Laguna de los Cerros demonstrates that the Olmec on the other hand were an entirely different animal so to speak. The construction of the temple mounds, stone sculptures, and ritual complexes found at these sites would have required significant resources and labor which could have only been organized by a very centralized society with narrowly delineated social positions and roles.

Archaeologists believe that the comparatively greater social complexity of the Olmec offered them a significant advantage in the mass production and distribution of goods, one that allowed them to achieve dominance in this early Mesoamerican exchange. Here it should be pointed out that "trade dominance" in this context is not what we would imagine it to be in today's society. The Olmec were not a gang of merchants who produced a lot of consumer goods which drove their competitors out of business. The Mesoamerican exchange is not generally thought of as something that had any immediate and significant impact on the day to day lives of most Mesoamericans. It is instead a phenomenon that exclusively involved the ruling elite of divergent societies found across Mesoamerica. Although not always explicitly visible in the archaeological record, the exchange of goods also entails a transference of ideas and particularly in the case of the Olmecs, the widespread trade of their ritual goods signifies the high esteem many Mesoamerican elites held for Olmec sensibilities and beliefs.

A recurrent theme in Mesoamerican culture is the use of exotic goods and foreign religious imagery as a means of legitimizing one's own rule and authority. For a long time Mesoamericanists have seen the widespread demand and adoption of Olmec aesthetic and material culture as the first expression of this theme. The general thinking is that elites coming from societies that were materially more humble than the Olmec would have been extremely impressed by the extravagance and grandeur of Olmec goods and culture, seeking to associate themselves with and ultimately emulate the behaviors and organizational patterns of the Olmec themselves. It is for this reason that the Olmec are widely considered to be the "Mother culture" of Mesoamerica. As the Olmec either directly or indirectly organized trade to distant regions and other Mesoamerican elites came to demand their ritual items, a pan-Mesoamerican elite culture began to develop - with certain religious practices and beliefs being adopted so completely across the region that a basic template for Mesoamerican civilization was established. Beliefs which were still widely observed by the time the Spanish arrived in Mesoamerica, like the worship of mountains and an early precursor to the Aztec rain god Tlaloc (God IV), reverence for the cardinal directions, and perhaps even the Mesoamerican Ballgame have their origins in Olmec religion. Although this narrative has been rightly critiqued by many (I myself am a firm believer that the Olmec were merely partners in the development of a shared Mesoamerican culture and that the contributions of the Zapotec have been grossly underestimated by Mesoamericanists) and there are competing explanations for the abundance of Olmec imagery in other Mesoamericans cultures, the basics of this interpretation are largely accepted by Mesoamericanists.

(Continued in reply)