Island biogeography is the study of the relationships between a variety of factors such as species populations, "island size", geographic distance, dispersal rates, and the like. These ideas have a long history and have been examined by many, including Darwin and Wallace in the 19th century to E.O.Wilson & MacArthur's work in 1963.
These ideas have since been applied to situations that have nothing to do with isolated islands in the sea. Man-made "islands" - such as isolated or fragmented habitats - are candidates for examination using the lens of islands biogeography. The pressures and dynamics are familiar: isolated habitats of varying distances, fragments of varying sizes, and varying numbers of different species. How will all these forces play out? This is what makes the study of island biogeography so interesting. I believe it has great relevance to anyone interested in the fate of the natural world in the 21st century - where so many habitats have been fragmented and degraded by human activity.
Some helpful links:
One notable example of these ideas is the study of the finches that occupy the Galapagos Islands that began with Darwin & Gould and continues to the present day - such as this genetic study from Harvard :
This website "Island Biogeography" gives some good background information about the history and concepts of island biogeography. They are also researching these ideas currently in the Caribbean:
Lastly, David Quammen's "The Song of the Dodo" is an excellent and readable book on the topic of island biogeography: