Evolutionary convergence is the use of one niche by organisms of different adaptive radiations. In a more general sense, evolutionary convergence occurs when two distinct species, usually unconnected to each other in any way, evolve over time to have many similar features.
Perhaps the strongest example of evolutionary convergence in the natural world is that of the Tasmanian wolf and the North American wolf. The Tasmanian wolf is a marsupial whose evolutionary history diverges greatly from that of the North American wolf, which is a mammal. Yet, in outward appearance, the two animals are very similar. They look the same, they behave similarly, and they hunt and feed in similar patterns.
Another marvelous example of evolutionary convergence is seen in that of the woodpecker. Several distinct variations of the modern woodpecker are found on various widely separated locales: the common flicker of North America, the honeycreeper of Hawaii, the huia in New Zealand, and the woodpecker finch of the Galapagos all fill nearly the same niche, but all evolved under wildly distinct circumstances. They all look nearly identical, with only minor differences in beak shape due to the different wood types available to dig into.
Evolutionary convergence is the result of an environment selecting a particular set of genes for a species over a period of time. A species slowly adapts to their environment, as survival of the fittest ensures that the members of that species best suited for a particular environment (or niche) will be the ones that prosper and pass on more genes than another. As a result, over a long period of time, two different species in similar environments will grow more similar, as the genes that make the species successful in that environment are selected for.
Outside of a biological context, evolutionary convergence also occurs in many other realms. In anthropology, it is often demonstrated that completely isolated cultures, over time, develop identical solutions to solve particular problems. This effect regularly occurs in research, where isolated pockets of researchers will develop an effective new technique, and then later discover that it was simultaneously developed by other researchers. The example of Gregor Mendel and Charles Darwin come to mind, as do Francis Crick and James Watson.
Evolutionary convergence seems to be the natural result of the survival of the fittest phenomenon; as a result, some form of evolutionary convergence will almost always occur in any situation where there is widespread survival of the fittest. Large-scale evolutionary models virtually always result in some sort of convergence, because quite often there is one "best way" of solving a problem, and through selection, that best way will be found.
Evolutionary convergence is just another way to describe and explain the observed world around us. It is a naturally occuring phenomenon that lends credence to the idea of survival of the fittest and occurs in many natural and social situations.