Yes, it's "number of prescriptions" (but not "number of people prescribed" or "number of doses"). One person could be prescribed an antibiotic (or multiple) several times a year.

I'm amazed that there are 1216 antibiotic prescriptions per 1000 people per year in West Virginia though (2.5x the rate of California or Colorado, which itself frankly seems pretty high). Are large parts of the South just awash with bacterial infections, are people being prescribed antibiotics for viral illnesses, or are they just taking antibiotics prophylactically?