It is used in the following way, given subsets of the sample space $$A_1, \cdots, A_n \subset \Omega$$ such that $\mathbb{P}(A_i) \leq \theta$.
Now define i.i.d. Bernoulli r.v.s $B_i \sim Ber(\theta)$, then $$(\chi_{A_1} , \cdots, \chi_{A_n}) \leq_{ST} (B_1, \cdots, B_n).$$
What does this $\leq_{ST}$ mean precisely?