Predation describes one species, the predator, feeding on and typically killing another organism, the prey species. Predators use various methods to capture prey, just as their prey use various methods to avoid capture. Herbivory is comparable to predation, but herbivores feed on plants rather than animals. Herbivores do not necessarily kill a plant they feed on but sometimes put pressure on the plant species.
Competition describes multiple organisms fighting for the same resources. Interspecies competition is competition between different species; intraspecies competition is competition between organisms of the same species.The competition may or may not involve active interference. Squirrels and deer may both eat acorns in a site but do not directly fight for the acorns and instead make fewer acorns available for the other. Alternatively, competition may involve direct interference, like when a plant secretes chemicals from its roots to keep other plants from growing around it. The more similar two species in a community are, the more competitive they are with each other, fighting for limited resources.
Parasitism is when one species benefits from a second species that is disadvantaged, but generally not killed. A tick feeding on a host is a good example of parasitism. The host is not directly killed by the tick, which benefits from the relationship while the host is adversely affected, as it feeds on the host's blood.
Mutualism is an interaction characterized by mutual benefit, so both species benefit from the relationship. A flowering plant producing nectar to attract an animal, such as a bee, is one example. The bee benefits by feeding on the nectar, while the plant benefits because the bee goes on to disperse the plant's pollen. Mutualism can also be thought of as "mutual exploitation."
Commensalism describes a relationship in which one species benefits but the other is unaffected. Examples of commensalism include a bird nesting in a tree. The bird is using the tree for shelter but the tree is unaffected. A second example is a certain intestinal bacteria species that lives in an animal's gut, which provides food and shelter for the bacteria, but the bacteria does not negatively or positively affect the host organism. Note that there are many types of intestinal bacteria, and while some -- commensalists -- have no affect on the host, others may benefit or harm the host.