The flu vaccine activates adaptive immunity. How does this occur?

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I believe it is a similar thing to natural selection, the ones less effected by it survive and adapt over time to survive the vaccine. However, google defines it this way, "The adaptive immune system, also known as the acquired immune system or, more rarely, as the specific immune system, is a subsystem of the overall immune system that is composed of highly specialized, systemic cells and processes that eliminate pathogens or prevent their growth"