Biodiversity is the variation that exists within a group and can be generalized to a population, ecosystem or the biosphere. Biodiversity is not consistent across the globe and it is dependent on genetic variation.
Think of the different types of biomes that exist (desert, tundra, tropical to name a few) and think of the types of organisms that live in these environments. Each environment hosts its own biodiversity and as you expand to the entire earth the diversity increases. The organisms best suited to live in each environment are able to survive and reproduce; increased ecological variation leads to increased biological diversity. As humans continue to destroy various environments biodiversity is lost.
Genetic variation leads to new adaptations and creates differences within a species and creates new species. Genetic variation is a result of sexual reproduction. Without sexual reproduction DNA would not be "mixed up" and therefore would not lead to differences with in species, natural selection and evolution which in turn would not develop a world rich in biodiversity.