A categorical position is a residency spot that includes the whole training program in a specialty, from PGY-1 to the final year, for example three years in internal medicine. If you match into a categorical position, you are expected to continue through the program, subject to meeting its requirements.
It differs from a preliminary position, which covers only one year and does not guarantee a place afterwards. Some specialties, such as radiology or anesthesiology, may ask applicants to secure a separate first-year position, so the structure varies by field and program.
Programs list the types of positions they offer in ERAS and in the NRMP Match. Read each program's description carefully.