The subject of the verb annuit, meaning he/she nods approval, is generally taken to be God Himself. The founding fathers wanted to emphasize the devine favor shown to the new nation.
The phrase is found on the Great Seal of the United States, from 1782, and appears to signify the favored status of the new country.
If you look carefully at any dollar bill you will find two more Latin phrases: Novus Ordo Seclorum and E Pluribus Unum.