early 13c., from Old French cloistre "monastery, convent; enclosure" (12c., Modern French cloître), from Medieval Latin claustrum "portion of monastery closed off to laity," from Latin claustrum (usually in plural, claustra) "place shut in, enclosure; bar, bolt, means of shutting in," from past participle stem of claudere (see close (v.)).
"The original purpose of cloisters was to afford a place in which the monks could take exercise and recreation" [Century Dictionary]. Spelling in French influenced by cloison "partition." Old English had clustor, clauster in the sense "prison, lock, barrier," directly from Latin, and cf. from the same source Dutch klooster, German Kloster, Polish klasztor.