The basis of evolutionary potential is clear enough in principle. Whether a population can evolve to cope with new circumstances depends on how much underlying genetic variation there is: do any individuals in the population have the genes to cope, even barely, with the new environment, or not? If not, everybody dies, and it’s game over. If yes, evolution may come to the rescue, improving, as time goes by, the ability of individuals to cope in the new environment. What determines the extent of the underlying genetic variation? Factors such as how big the population is (bigger populations usually contain more genetic variation) and how often mutations occur.
Let me give an example of how this works. Imagine you have a population of algae that have been living for generations in a comfy freshwater pool. Now suppose there’s a ghastly accident and, all of a sudden, the pool becomes super-salty. Whether the algae will be able to survive depends on whether any individuals already have any capacity to survive and reproduce in salty water. If none of them do, they all die, and the population goes extinct. But if some do, then the survivors will reproduce, and over time, beneficial mutations will accumulate such that the algae get better and better at living in a high-salt environment.
This isn’t just hypothetical: many experiments have taken organisms, be they algae, fungi or bacteria, from an environment to which they are well-adapted to one where they are not, and watched what happens. The result is reliable: at first, they tend not to cope that well (measured, as usual in evolution, by their ability to survive and reproduce). However, as long as the environment doesn’t change again, their coping ability rapidly improves: within a few tens of generations, beneficial mutations appear and spread, and the organisms evolve to become much better at handling their new circumstances.
But here’s the thing. A big drawback of experiments of this type is that the initial change the organisms experience is not that severe — it is not, in fact, so severe that no one can cope, and the population goes extinct.