In ecology, the species that has the most presence in a given ecological system. This can be measured by numbers, biomass, land coverage, or the amount of energy flowing through that species. As you might expect, dominant species are generally plants; all solar energy must pass through them first.
In many ecosystems there are a number of co-dominant species. Dominant species may be referred to in relation to their position in the food web. Thus you might have bison as the dominant species on the level of primary consumers, and humans dominant as a secondary consumer.
Related ideas are primary producers, keystone species, food web, and The trophic cascade hypothesis.
I have found a bird watching dictionary that uses dominant species to mean a species that dominates, through physical action, over another; the dominant species is the one that wins all the fights, over food or territory. I have found other on-line dictionaries that have definitions along the lines of "A species within a given environment that exerts much influence on other species, and is most likely at the top of the food chain".