A frequentist two-word answer: Relative frequencies.

Popper’s two-word answer: Experimental propensities.

A QBist two-word answer: Nothing does.

My two word-answer: We do.

My one-paragraph answer: The objectivity of Born probabilities is not constituted by their correspondence to or representation of anything in the physical world (such as a relative frequency, or a property of an entire experimental arrangement). The objectivity of a Born probability is instituted by the community of physicists and others when applying quantum theory. To accept quantum theory is to adopt a practice of that community—the practice of conforming one’s opinions to two norms governing this practice. One norm governs the doxastic state of a practitioner who applies the Born Rule. The other norm circumscribes the situations for which the Born Rule may be legitimately applied.