AABB-pattern reduplication of
世代 ('generation; era'). Both
世 and
代 mean roughly 'generation' on their own — doubling each up emphasizes continuity across an unbroken chain of generations. It functions as an adverb:
世世代代 + verb. Common collocations:
世世代代相传 ('passed down through the generations'),
世世代代生活在 ('have lived for generations in').