The empire you are referring to is the Aztec Empire (or Mexica Empire). It was a powerful Mesoamerican civilization that dominated large parts of what is now central and southern Mexico during the 15th and early 16th centuries. The Aztec Empire was known for its advanced agricultural practices, impressive architectural achievements, and complex social and political structures.
The empire came to an end following the Spanish conquest led by Hernán Cortés in 1519-1521. The conquest resulted in the fall of Tenochtitlán, the Aztec capital, and the establishment of Spanish colonial rule in the region.