mid-13c., suster, "female sibling, a female person in her relation to other children of the same parents," from Old English sweostor, swuster, Northumbrian soester "sister," or a Scandinavian cognate (Old Norse systir, Swedish syster, Danish søster), in any case from Proto-Germanic *swestr- (source also of Old Saxon swestar, Old Frisian swester, Middle Dutch suster, Dutch zuster, Old High German swester, German Schwester, Gothic swistar).
These are from PIE *swesor, one of the most persistent and unchanging root words, recognizable in almost every modern Indo-European language (Sanskrit svasar-, Avestan shanhar-, Latin soror, Old Church Slavonic, Russian sestra, Lithuanian sesuo, Old Irish siur, Welsh chwaer). Greek eor "daughter, cousin" is the surviving relic of the root in that language, perhaps from a dialectal vocative form; it was replaced as "sister" byadelphē (for which see Adelphi).French soeur "a sister" (11c., instead of *sereur) is directly from Latin soror, a rare case of a borrowing from the nominative case.
The forms in -u- persisted through Middle English; for the vowel evolution, see bury. It was used of nuns in Old English, of the Fates from c. 1300, the Muses from late 14c., and of the Pleiades from early 15c.
From late 14c. as "fellow woman," without regard to relationship, "fellow creature, woman sharing the human condition," also "woman engaged in the same activity as another." The meaning "female fellow-Christian, woman of one's own faith" is from mid-15c. In modern use, of a woman in general from 1906; especially in U.S. of "a Black woman" from 1926; and in the sense of "fellow feminist" from 1912. Sister act "variety act by two or more sisters" is from vaudeville (1908).