It's a "wedding token" - a popular issue that is given away at weddings. Usually has depictions of Maximilian and Carlota, as their love was rumored to be pure (which was very unusual for royal marriages at the time), but there are also examples with Agustin de Iturbide (your example), Benito Juarez and Aztec imagery. It's not from 19th Century, though. A lot of those were struck in the 50's and some are still being produced today.
Mike Locke had a nice write-up on these, but the site seems to be taken down.
A-ha! Internet Archive to the rescue:
https://web.archive.org/web/20130305070724/http://www.calgoldcoin.com/mexico.htmYour looks to be the example catalogued as "1823 Augustinus #2, same overall design as #1, but both dies slightly different."