Most relatively primitive civilizations from millennia ago had a nearly spiritual relationship with the animals that lived around them. For the Olmec, some of these included eagles, jaguars, caiman, sharks, and snakes. These are things that they would have come across on a regular basis and undoubtedly believed to have considerable power.
Just as the ancient Egyptians had Falcons and jackals represented in their gods and goddesses, the Olmec had unique holy combinations. A human-jaguar being may have representative their primary god that have power over all the others. Various statues of these have been discovered in situations that depict their unique power.
Other information about their belief systems includes a dragon-like creature that lived in the sky, and a collection of numbered gods that did not particularly have names. The dragon there is a very similar appearance to Quetzalcoatl, who was revered by the Aztec in later years. Of course, since there are not any written documents telling stories or listing prayers that people used to worship these deities, they may have had names that are now lost to history.