Saaeculum is a second declension noun, usually the accusative case saecula following a preposition, and meaning race, breed, generation, lifetime.
Saeculorum is the genitive plural of saeculum. The genitive case is the Latin grammatical case of possession that marks a noun as being the possessor of another noun. For example, discupuli servorum means “servants’ disciples”.
According to the calculation of the Etruscans, which was adopted by the Romans, a saeculum was a space of time containing 110 lunar years.
The phrase “unto the ages of ages” expresses either the idea of eternity or an indeterminate number of aeons. The phrase is a translation of the original Koine Greek phrase “εἰς τοὺς αἰῶνας τῶν αἰώνων”, in the Latin alphabet “eis toùs aionas ton aiṓnōn”. The phrase occurs in the original Greek texts of the New Testament.
In the Latin Vulgate, the phrase is translated as “in saecula saeculorum” and in the English Douay Rheims as “world without end”.
As Wikipedia points out, “For over a thousand years (c. AD 400–1530), the Vulgate was the most commonly used edition of the most influential text in Western European society.”
Neither you nor I did any of the hard work. Thank you, Jerome, for going to Jerusalem, and thank you, men of Douay and Rheims.