How are the concepts of species, population, and community related?

Species, population, and community are concepts commonly studied in ecology. They are sometimes called levels of organization in ecology. 

A species refers to individual organisms that can reproduce and produce fertile offspring. For example, horses belong to their own species. They can reproduce and their offspring can reproduce. Donkeys are their own species for the same reason. However, if a horse breeds with a donkey the offspring, a mule, is not fertile. Since the mule...

Species, population, and community are concepts commonly studied in ecology. They are sometimes called levels of organization in ecology. 

A species refers to individual organisms that can reproduce and produce fertile offspring. For example, horses belong to their own species. They can reproduce and their offspring can reproduce. Donkeys are their own species for the same reason. However, if a horse breeds with a donkey the offspring, a mule, is not fertile. Since the mule cannot produce offspring, it is a not a species. This also provides evidence that a horse and donkey are two separate species. The process of determining what constitutes a species can get very complicated, especially when working with plants. The example I've provided is part of the biological species concept and is a common way to define a species.

A population is a collection of all of the members of a specific species in a given area. For example, all of the walleye in a lake can be considered a population. A population will contain its own genetic variation, and there will also be genetic variation between different populations. If a population is isolated from other populations over long periods of time, they may become so genetically different that they become their own species. 

A community includes all of the populations of living organisms in a given area. For example, the collection of all living organisms in the lake with the walleye is a community. At the community level of ecology we begin to see many different interactions happen between different species. Common interactions include predator-prey interactions, competition, and symbiosis. At the community level we can also observe food webs and study how energy flows through an environment. Communities with higher levels of diversity are usually considered more stable and resilient to disturbances than communities with low levels of diversity.

In short, a individuals of a species are part of a population, and a population is part of a community.