Let's be clear on this. It's not even one phrase.
'Annuit Coeptis' is clearly seperate from the rest, and it means 'Providence favours what we do."
'Novus Ordo Seclorum' means "A New Era of the Ages" or "A new time of generartions." It refers to the new form of Government the Ameircans wanted to set up after the Revolution.
'Seclorum' means Ages, or generations- that kind of 'time passing' sense. It does not even vaguely mean 'secular'.
As ever, Deano is posting sources that are full of shit.