Here, it has to do with the development of current forms of life from earlier forms, including common ancestry relationships. Examples would include the evolution of modern dogs and wolves from a common ancestor, or the evolution of amphibians from fish. Note that this definition says nothing about the mechanism by which these species developed from their common ancestors. A third meaning is in specific reference to Darwin's theory of evolution. Since this theory is often misunderstood, it is worth explaining briefly.
Darwinian evolution has two fundamental pieces.
Over time, this combination of genetic variation and natural selection produces new species. On a small scale, Darwin's theory has been well verified. Directly observed examples include the evolution of bacteria resistant to certain drugs. For species that reproduce over longer timescales, the inferences for evolution must be made less directly. But it is now quite clear that, at least on some scales, Darwinian mechanisms are indeed a valid description of nature.