PGY stands for postgraduate year. It counts the years of graduate medical education since medical school. PGY-1 is the first year of residency (often called the intern year), PGY-2 is the second, and so on. Programs are described by their length, so a three-year internal medicine residency runs from PGY-1 to PGY-3.
PGY level reflects training stage, not age or time since graduation, and it often determines supervision, responsibility and pay scale at a hospital. Applicants to a first-year position are often described as applying for PGY-1.
Some specialties begin with a preliminary year and others include the first year within the program, so the position type (categorical or preliminary) affects what happens after PGY-1. Residency positions are filled through the NRMP Match.