In this paper, we describe factor representations of discrete 2-step nilpotent groups with 2-divisible center in the spirit of the orbit method. We show that some standard theorems of the orbit method are valid for these groups. In the case of countable 2-step nilpotent groups we explain how to construct a factor representation starting with an orbit of the "coadjoint representation." We also prove that every factor representation (more precisely, every trace) can be obtained by this construction, and prove a theorem on the decomposition of a factor representation restricted to a subgroup. Bibliography: 7 titles.