The statement is a short one, but it manages to sum up what happens in nature in a simplified manner.
All the species have evolved to a certain type of environment, thus being perfectly well adapted to certain living conditions, and developing traits that are advantageous for the survival in that particular environment. But the Earth is constantly changing, and those changes result in changes of the environment, sometimes gradually, sometimes very quickly. The loss or change of environment always has huge impact on the species. Some go extinct, especially the ones that have been too specialized, while the more opportunistic and less specialized species often manage to survive. The ones that manage to survive face a new environment, so they evolve in a way that is advantageous for them to survive in the new environment, thus giving rise to new species. Other species may already have the required traits for the new environment but have been living in different area, so they will gradually move in this new environment as it suits them, thus having a situation where the ecosystems will eventually be totally changed and unrecognizable from the predeceasing ecosystems.
