This medal is described as an "Illuminati coin". You're all experts. What is it REALLY? Answer in about 2 hours if nobody nails it. https://www.auctionzip.com/auction-lot/ILLUMINATI-coin.-Proof._4ED4519A61/
Or "The Great Seal of the United States", to be extremely accurate. Most people have no idea the Great Seal is two-sided.
That's what you get when you watch too many movies. The Cradle of Life with Angelia Jolie against the power crazed Illuminati. Guess who won. lol
Actually it should be called "The Eye of Providence" or "the all-seeing eye of God", which has a lot less omninous meaning than the "Illuminati".
The one in the OP appears to be a modern copy (sort of) of a medal struck in 1882 for the centennial of the Great Seal. I can't find pics of one I'm sure is an original, but the Mint restruck them in the 20th century. Barber's design had a characteristically "Barberesque" eagle on it, while the one in the OP link seems to have a modernized eagle. So it's just some modern proof widget, I reckon.