lowest noncommissioned army officer, 1570s, from French corporal, from Italian caporale "a corporal," from capo "chief, head," from Latin caput "head," also "leader, guide, chief person" (from PIE root *kaput- "head"). So called because he was in charge of a body of troops. Perhaps influenced by Italian corpo, from Latin corps "body." Or corps may be the source and caput the influence, as OED suggests.
Earlier it meant "a communion cloth" (late 14c.), from Medieval Latin corporalis (palla).
late 14c., "material, physical; secular;" c. 1400, "of or belonging to the body;" from Old French corporal (12c., Modern French corporel) "of the body, physical, strong" and directly from Latin corporalis "pertaining to the body," from corpus (genitive corporis) "body" (from PIE root *kwrep- "body, form, appearance").
Corporal punishment "punishment of the body" (as opposed to fine or loss of rank or privilege) is from 1580s. Related: Corporality.