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"Vector" has several meanings, such as a mathematical idea, or an "infection carrier". Since you mention population evolution, which is treated mathematically, I will assume you mean the former.

A vector is an ordered set of numbers, such as the relative population levels of various different genotypes or phenotypes. One can think of the vector as a direction in a high dimensional abstract space. As populations evolve, these relative levels change (in response to natural selection), so the direction of the corresponding vector changes, roughly towards a direction that maximizes the total population number (if the environment itself is not changing). This increases overall "fitness".

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