The image on the Mexican flag comes from an Aztec vision

In the fourteenth century, a group of Chichmecas (warrior nomads) called the Aztecs (or Mexicas) settled in Mexico when they saw an eagle (representing the sun) standing on a cactus (a symbol of the heart) clutching a snake (a symbol of the earth or Quetzalcoatl)—an image which is now depicted on the Mexican flag.
The official name of Mexico is Estados Únidos Mexicanos
Don't be surprised if you get funny looks when you tell people in Mexico . . .