Stan is exceptional if what you need is a hierarchical Bayesian model, and if what you want is rigorous way of quantifying the uncertainty associated in the parameter selections in your model.

Stan users are more often R users than Python user and mostly come from science backgrounds. They often use Stan via a package called BRMS which stands for "Bayesian Regression Models using Stan" which should give you some idea of its core use case.

You wouldn't use Stan if you weren't trying to model your problem as a distribution based probabilistic model.