"to draw air into and expel it from the lungs; to inhale and exhale (a scent, etc.)," c. 1200, not in Old English, but it retains the original Old English vowel of its source word, breath. To breathe (one's) last "die" is from 1590s. To breathe down the back of (someone's) neck "be close behind" is by 1946. Related: Breathed; breathing.
The original long vowel (preserved in breathe) has become short. Meaning "ability to breathe," hence "life" is from c. 1300. Meaning "a single act of breathing" is from late 15c.; sense of "the duration of a breath, a moment, a short time" is from early 13c. Meaning "a breeze, a movement of free air" is from late 14c.
late 14c., respiren, "breathe, draw breath," from Old French respirer (12c.) and directly from Latin respirare "breathe again, breathe in and out," from re- "again" (see re-) + spirare "to breathe" (see spirit (n.)). Formerly also "to rest or enjoy relief after toil or exertion" (1590s). Related: Respired; respiring.
c. 1400, exale, transitive, originally of liquids, perfumes, the breath of life, etc., from Old French exhaler (14c.) and directly from Latin exhalare "breathe out, evaporate," from ex "out" (see ex-) + halare "breathe." Of living things, "to breathe out," 1580s transitive; by 1837 intransitive. Related: Exhaled; exhaling.
c. 1400, "to die," from Old French expirer "expire, elapse" (12c.), from Latin expirare/exspirare "breathe out, blow out, exhale; breathe one's last, die," hence, figuratively, "expire, come to an end, cease," from ex "out" (see ex-) + spirare "to breathe" (see spirit (n.)). "Die" is the older sense in English; that of "breathe out" is attested from 1580s. Of laws, patents, treaties, etc., mid-15c. In 17c. also transitive. Related: Expired; expiring.
late 14c., respiracioun, "act or process of breathing, inhalation and exhalation of air by the lungs," from Latin respirationem (nominative respiratio) "breathing, respiration," noun of action from past-participle stem of respirare "breathe again, breathe in and out," from re- "again" (see re-) + spirare "to breathe" (see spirit (n.)). Extended to plants by 1831. Milton used it for "act of returning to life" ("breathing again").