In the field of ecology, a consumer is any member of a food chain that gets its energy from consuming other organisms. A producer is an organism that produces or collects its energy from inorganic compounds. Primary consumers are those consumers that get their energy by consuming producers, and are thus the second link in the food chain (AKA the second trophic level).
Primary consumers include animals (herbivores), bacteria, microbes, and fungus (decomposers), and the occasional plant (parasitic plants and carnivorous pants).
Primary consumers are often an important limiting factor on primary producers; large herbivorous may overgraze grasses, plagues of insects may destroy forests, and urchins can destroy a kelp forest -- if they get out of hand. On the other hand, consumers have been around for billions of years, and producers have always depended on them as important parts of their life-cycles, using them to limit population growth, decompose dead organisms and provide fertilizer, pollinate, and carry seeds.
Those beings that eat primary consumers are called secondary consumers, and those that feed on the secondary consumers are the tertiary consumers. In actuality, there are many organisms that alternate between trophic levels, including humans, and will be a primary consumer or a secondary (or higher) consumer depending on what is put before them.