A literary or formal expression meaning 'for generations without end', often used in poetic, religious, or solemn contexts. Not common in everyday speech.
末永く means 'for a long time to come' and is used in well-wishing (e.g., 末永くお幸せに). 世々限り無く is more solemn and implies an unending span across ages.
Etymology
Compound of 世々 (yoyo, 'generations, ages') + 限り無く (kagirinaku, 'without limit'). The exact historical derivation is uncertain, but it follows a classical pattern of adverbial phrases expressing perpetuity.