The Aztecs were a group of people who ruled the aptly named Aztec Empire. The Aztec empire occupied most of Mexico, from around Aguascalientes to Guatemala. They were very famous warriors until they got their collective butts kicked by a band of desperate spaniards who had their ships burnt by Hernan Cortez, their leader. They also had horses, gunpowder and metallic armor, so that helped. :-)
That bloody mess was the birth of today's Mexico.