Mutualism is a relationship between two organisms in which both benefit. It is a type of symbiosis which improves the biological fitness of both parties. The two organisms usually come from widely different types, often from different phyla or even kingdoms. The term is not used for any cooperation between animals of the same species.
Edouard van Beneden (1809–1894) introduced the term into evolutionary biology and ecology in the 1870s.
Many relationships between insects and flowering plants, where the insect gets food, and the plant gets transfer of pollen.
Gut flora: many relationships between gut bacteria and herbivores. The bacteria digest cellulose, and get a regular supply of nutrients. Almost no animal can digest cellulose by itself.
Lichen: an extremely close relationship between algae and fungi. Probably a mutualistic relationship, but less clearly.
Figs: each fig tree species is pollinated by its own wasp species.
Cleaner fish: small fish which pick parasites and dead matter from the mouth and body of much larger fish. The larger fish responds to the 'dance' of the cleaner by going passive.
References
↑Boucher D.H. 1985. The idea of mutualism, past and future. In D.H. Boucher (ed) The biology of mutualism: ecology and evolution. Oxford University Press. 1–28