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A niece is defined as the daughter of one's brother or sister.
Literal
Niece [called-とは] brother [possessive-の] daughter [object-を] call.
とは is the definitional marker — 'X is defined as, X means.' Often at the start of dictionary or textbook definitions. 言う ('to call, to say') in this frame means 'to be called, to refer to as.' 兄弟 ('brothers') in older usage can refer to siblings of both genders, so 兄弟の娘 ('the daughter of one's siblings') covers both nieces on the brother's side and on the sister's side.