ints means that both int and int[] arrray are supported. The full list of supported signatures for the poisson_lpmf function is:

poisson_lpmf(int, real) => real
poisson_lpmf(int, vector) => real
poisson_lpmf(int, row_vector) => real
poisson_lpmf(int, array[] real) => real
poisson_lpmf(array[] int, real) => real
poisson_lpmf(array[] int, vector) => real
poisson_lpmf(array[] int, row_vector) => real
poisson_lpmf(array[] int, array[] real) => real

So this is just a shorthand so that we dont need to write eight signatures in the documentation. reals similarlly mean that real, real[], vector and row_vector are supported.