Mutualism is a form of symbiosis, where two species have evolved to have a mutually-beneficial close relationship, so close that basically one cannot live without the other. There are many examples of this type of symbiosis in the natural world, such as the Yucca plant and the Yucca Moth, the Acacia tree and a species of ant (I can't recall which one.) Etc.
Mutualism differs from Commensalism, which is where two species live in a symbiotic relationship that benefits one while neither benefitting nor harming the other. The good example here is humpback whales and the barnacles that live on the whale's skin. The barnacles get a free ride around the ocean, happily filter-feeding the whole way, while the whales receive no benefit, but they are not harmed either.
Then of course there is parasitsm, but I think we all know about this one.