niece (n.)

c. 1300, nece, "daughter of one's brother or sister; granddaughter; female relative," from Old French niece "niece; granddaughter" (12c., Modern French nièce), earlier niepce, from Latin neptia (also source of Portuguese neta, Spanish nieta), a more decidedly feminine form of neptis "granddaughter," in Late Latin "niece," fem. of nepos "grandson, nephew" (see nephew). Cognate with Old Lithuanian neptė, Sanskrit naptih "granddaughter;" Czech net, Old Irish necht, Welsh nith, German Nichte "niece." 

It replaced Old English nift, from Proto-Germanic *neftiz, from the same PIE root (Old English also used broðordohter and nefene). Until c. 1600 in English, niece also commonly meant "a granddaughter" or any remote female descendant or kinswoman.