Annuit cœptis (pron.: / /; in classical Latin: [ˈannwɪt ˈkojptɪs]) is one of two mottos on the reverse side of the Great Seal of the United States. (The second motto is Novus ordo seclorum; another motto appears on the obverse side of the Great Seal: E pluribus unum).
Taken from the Latin words annuo (third-person singular present or perfect annuit), "to nod" or "to approve", and coeptum (plural coepta), "commencement, undertaking", it is literally translated, "He approves (has approved) of the undertakings".
On the Great Seal 
In 1782, Sam Adams created the third Congress and appointed a design artist, William Barton of Philadelphia, to bring a proposal for the national seal. For the reverse, Barton suggested a thirteen layered pyramid underneath the Eye of Providence. The mottos which Barton chose to accompany the design were Deo Favente ("with God's favor", or more literally, "with God favoring") and Perennis ("Everlasting"). The pyramid and Perennis motto had come from a $50 Continental currency bill designed by Francis Hopkinson.
Barton explained that the motto alluded to the Eye of Providence: "Deo favente which alludes to the Eye in the Arms, meant for the Eye of Providence." For Barton, Deus (God) and The Eye of Providence were the same entity.
When designing the final version of the Great Seal, Charles Thomson (a former Latin teacher) kept the pyramid and eye for the reverse side but replaced the two mottos, using Annuit Cœptis instead of Deo Favente (and Novus Ordo Seclorum instead of Perennis). When he provided his official explanation of the meaning of this motto, he wrote:
"The Eye over it [the pyramid] and the motto Annuit Cœptis allude to the many signal interpositions of providence in favor of the American cause."
The Change from Deo Favente to Annuit Coeptis 
T. Jeremy Gunn, a director for the ACLU, argues that a more accurate translation is "our undertakings have been favored," leaving the reader to infer who or what was responsible for favoring such undertakings. Gunn maintains that had Congress wished to include the literal word "God" the correct translation would have been, "Deo Favente." Robert Hieronimus, who wrote a Ph.D. dissertation about this portion of the Great Seal, argued that Thomson's intent was to find a phrase that contained exactly 13 letters to fit the theme of the seal. On the obverse was E Pluribus Unum (13 letters), along with 13 arrows, 13 stars, and 13 stripes. The pyramid under the motto, Annuit Coeptis, has 13 levels. "Deo Favente" had only nine letters. According to Hieronimus, Annuit Coeptis, has 13 letters and was selected to fit the theme. Others have maintained that the 13 letters in E Pluribus Unum and Annuit Coeptis are mere coincidences. 
Classic Source of the Motto 
According to Richard S. Patterson and Richardson Dougall:
Annuit cœptis and the other motto on the reverse of the Great Seal, Novus ordo seclorum, can both be traced to lines by the Roman poet Virgil. Annuit cœptis comes from the Aeneid, book IX, line 625, which reads, Jupiter omnipotens, audacibus annue cœptis. It is a prayer by Ascanius, the son of the hero of the story, Aeneas, which translates to, "Jupiter Almighty, favour [my] bold undertakings."
- MacArthur, John D. (2011). "E Pluribus Unum" <www.greatseal.com>. Retrieved 11-25-2011.
- MacArthur, John D. (2011). "Annuit Coeptis" <www.greatseal.com>. Retrieved 11-25-2011.
- MacArthur, John D. (2011). "Third Committee" <www.greatseal.com>. Retrieved 11-25-2011.
- MacArthur, John D. (2011). "Third Great Seal Committee–May 1782" <www.greatseal.com>. Retrieved 11-25-2011. The note can be seen here, and the pyramid portion here.
- Papers of the Continental Congress, item 23, folios 137-139.
- Journals of the Continental Congress, June 1782
- U.S. Department of State, Bureau of Public Affairs (2003). "The Great Seal of the United States" <www.state.gov>. Retrieved 11-25-2011.
- Bureau of Engraving, Currency Notes
- U.S. Treasury (2010). "Portraits & Designs" <www.treasury.gov>. Retrieved 11-25-2011.
- T. Jeremy Gunn, "Religious symbols and expressions in the public square." In The Oxford Handbook of Church and State in the United States. New York: Oxford University Press, 2010
- Robert Hieronimus, Founding Fathers
- Snopes, Hayim Solomon
- Vergilius Maro, Publius (29 - 19 BC). Aeneid. <www.thelatinlibrary.com>. Retrieved 11-25-2011.