c. 1200, persoun, "an individual, a human being," from Old French persone "human being, anyone, person" (12c., Modern French personne) and directly from Latin persona "human being, person, personage; a part in a drama, assumed character," originally "a mask, a false face," such as those of wood or clay, covering the whole head, worn by the actors in later Roman theater. OED offers the general 19c. explanation of persona as "related to" Latin personare "to sound through" (i.e. the mask as something spoken through and perhaps amplifying the voice), "but the long o makes a difficulty ...." Klein and Barnhart say it is possibly borrowed from Etruscan phersu "mask." De Vaan has no entry for it.
From mid-13c. as "one of the persons of the Trinity," a theological use in Church Latin of the classical word. Meanings "one's physical being, the living body; external appearance" are from late 14c. In grammar, "one of the relations which a subject may have to a verb," from 1510s. In legal use, "corporate body or corporation other than the state and having rights and duties before the law," 15c., short for person aggregate (c. 1400), person corporate (mid-15c.).
The use of -person to replace -man in compounds for the sake of gender neutrality or to avoid allegations of sexism is recorded by 1971 (in chairperson). In person "by bodily presence" is from 1560s. Person-to-person is attested by 1919, originally of telephone calls.