Biodiversity
Biodiversity is understood to be endemic to the health of wild environments, and should be cherished, protected and preserved to maintain a healthy environment. Many who study biodiversity make special note of the periodic extinctions of living organisms over millions of years.
Alpha Diversity
Alpha diversity is usually what people are referring to when they talk about "biodiversity" --- that is, the biodiversity of a particular and distinctive type of environment, like a subtropical rainforest or a lake. This is measured by noting the number of different types of species, families and organisms in this environment.
Beta Diversity
Beta diversity compares the biodiversity of one environment as compared to adjacent or related environments. The metric of beta diversity is the amount of unique species as compared to unique species in another environment. This is usually expressed as an integer on a scale of one to 10.
Gamma Diversity
Gamma-level diversity is the cumulative diversity in a region of geographical distinction --- either natural, like an island, or arbitrary, like the state of Connecticut. This number is usually expressed as the sum of a group of ecosystems that have been measured and compared through alpha and beta diversity algorithms.