Old English pursa "little bag made of leather," especially for carrying money, from Medieval Latin bursa "leather purse" (source also of Old French borse, 12c., Modern French bourse; see bourse), from Late Latin bursa, variant of byrsa "hide," from Greek byrsa "hide, leather." Change of b- to p- perhaps by influence of Old English pusa, Old Norse posi "bag."
Meaning "woman's handbag" is attested from 1951. Meaning "sum of money collected as a prize in a race, etc.," is from 1640s. Purse-strings, figurative for "control of money," is from early 15c. Purse-snatcher first attested 1902 (earlier purse-picker, 1540s). The notion of "drawn together by a thong" also is behind purse-net (c. 1400).