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Your guess sounds plausible. I do wonder why is it not called "years" instead of "ages" then.
After doing some digging in the code, I found out that the concept of ages primarily has to do with a method for FreeCol's AI to select which founding Fathers to displays as options for the player to pick.
The ages are roughly from game start (normally 1492) to the year 1599, a second from 1600-1699, and the final of the three starts at 1700.
The decision to call them ages probably, and I am speculating, just simply to denote these longer periods of times (at least a century) with one simple word.