Which measure is estimated in cross-sectional data when Poisson regression with robust standard errors is used?

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In cross-sectional data with a binary outcome, Poisson regression with robust standard errors estimates the prevalence ratio. Here, the outcome is measured at a single time point, so the relevant measure of association is how the probability (prevalence) of the outcome differs between exposure groups. The model uses a log link, and the exponentiated coefficients correspond to the ratio of prevalences for a unit change in the predictor. The robust standard errors adjust for the fact that a Poisson variance assumption isn’t correct for a binary outcome, making the inference valid. So the result you get is a prevalence ratio, reflecting how much more (or less) prevalent the outcome is in one group compared with another.