The youngest daughter is always given a third of the apple.
Literal
End's daughter [to-には] always apple's three-division's one [subject-が] is-given.
末 ('end, last') in family contexts refers to the youngest — 末の娘 ('end daughter' = youngest daughter), 末っ子 ('youngest child'). 3分の1 is the Japanese format for fractions: '[denominator]分の[numerator].' The passive 与えられる frames the daughter as the recipient without specifying the giver.