niece (n.)

c. 1300, neveu, "son of one's sister or brother," also "a grandson; a relative; a kinsman," from Old French neveu (Old North French nevu) "grandson, descendant," from Latin nepotem (nominative nepos) "sister's son, grandson, descendant," in post-Augustan Latin (c. 150 A.D.), "nephew," from PIE *nepot- "grandchild," and in a general sense, "male descendant other than son" (source also of Sanskrit napat "grandson, descendant;" Old Persian napat- "grandson;" Old Lithuanian nepuotis "grandson;" Dutch neef; German Neffe "nephew;" Old Irish nia, genitive niath "son of a sister," Welsh nei).

The original pronunciation is /nev-u/; the spelling was changed unetymologically to -ph- after c. 1400, and the pronunciation partly followed it. Used in English in all the classical senses until the meaning narrowed in 17c., and also as a euphemism for "the illegitimate son of an ecclesiastic" (1580s). The Old English cognate, nefa "nephew, stepson, grandson, second cousin" survived to 16c.

[I]ts final exclusive use for 'nephew' instead of 'grandson' is prob. due in part to the fact that, by reason of the great difference in age, a person has comparatively little to do with his grandsons, if he has any, while nephews are proverbially present and attentive, if their uncle is of any importance. [Century Dictionary]