The unit rank is a cosmetic rating. It is found in the information panel when selecting a unit.
StarCraft
In StarCraft, terran units have ranks. Heroes have higher ranks than their base unit. Certain units like civilians do not have ranks, and a few heroes like Jim Raynor can have non-standard ranks (Raynor is labelled "marshal", for instance, a law enforcement rank rather than a military rank).
In StarCraft II, units that may attack may gain rank by making kills. Some hero units have static unique ranks; for instance, Tychus Findlay's rank is "scoundrel".