I pointed out Forrest McDonald's book for the very reason that you really need to understand the term in the context of the eighteenth century and the first century B.C. to wit:
The motto has been traced to Virgil, the renowned Roman poet who lived in the first century B.C. to a line in his Eclogue IV, the pastoral poem that expresses the longing of the world for a new era of peace and happiness.
"Magnus ab integro seclorum nascitur ordo."
Virgil's line has been translated in different ways, including:
The great series of ages begins anew.
The ages' mighty march begins anew.
A mighty order of ages is born anew.
The majestic roll of circling centuries begins anew.
The entire passage by Virgil reads:
Ultima Cumaei venit iam carminis aetas;
magnus ab integro saeclorum nascitur ordo.
iam redit et Virgo, redeunt Saturnia regna,
iam nova progenies caelo demittitur alto.
I hope this helps you to better understand the phrase.