mid-14c., "female spinner of thread," from Middle English spinnen "spin fibers into thread" (see spin (v.)) + -stere, feminine suffix (see -ster). Unmarried women were supposed to occupy themselves with spinning, hence the word came to be "the legal designation in England of all unmarried women from a viscount's daughter downward" [Century Dictionary] in documents from 1600s to early 1900s, and by 1719 the word was being used generically for "woman still unmarried and beyond the usual age for it."
Spinster, a terme, or an addition in our Common Law, onely added in Obligations, Euidences, and Writings, vnto maids vnmarried. [John Minsheu, "Ductor in Linguas," 1617]
Strictly in reference to those who spin, spinster also was used of both sexes (compare webster, baxter, brewster) and so a double-feminine form emerged, spinstress "a female spinner" (1640s), which by 1716 also was being used for "maiden lady." Related: Spinsterhood.