The Aztecs, a nomadic people, came relatively late on the scene in Mexico. They arrived in the Valley of Mexico sometime in the mid-1200's, by which time all the good land seems to have been claimed by their stronger, push-you-in-the-nose, tribute-demanding neighbors.
Undaunted, the Aztecs established themselves in a place no one else cared about or wanted -- namely, in the middle of a swampy area in the north-western fringe of Lake Texcoco. The only decent dry land available to them here was a small island. According to legend, Huitzilopochtli, the Aztec war chief, sent his men out on what would seem to be a fool's errand: to find the missing heart of a defeated enemy named Copil. At some point, someone inspecting the island noticed something unusual. History does not record his name, so let us name him Herbert. What Herbert saw was an eagle on top of a cactus with a snake in its claws. Ah, thought Herbert, a clear sign from the gods, no doubt, so back to his war chief he ran, ready to burst with the news. This, then, was to be the site where Huitzilopochtli, Herbert and the other Aztecs would erect their settlement and from whence their empire would spring.
The year was 1325, and now, almost 700 years later, this eagle-and-snake pair seen on the cactus is still used as Mexico's national symbol, appearing on the Mexican flag and currency, for example.
Tenochtitlán was one of the great cities of its day. At the time of the Spanish arrival in the early 1500's--which, as with everywhere else they went, would spell doom and chaos for the empire-- the metropolitan population of Tenochtitlán was estimated to be 200,000. This made it larger than any city in Europe at the time.
As far as the Aztecs were concerned, an imperialistic step in the right direction was made in the year 1375, when they elected an absolute ruler. Among the first words uttered by their new ruler was something like, "Anybody else feel like some imperialistic expansion?"
The early Aztec rulers furthered their power base by marrying into other lineages such as that of the influential Toltecs. Before long the Aztecs had absorbed all of the great cities of the Valley of Mexico, and would then spread their power further afield, eventually controling land bordering the Gulf of Mexico to the east as well as the Pacific Ocean to the west, and down to as far south as modern-day Ecuador.
Meanwhile, as tribute flowed into the Aztec capital, radical changes were taking place in Tenochtitlán. A time-traveling visitor in 1345 would hardly have recognized the place in, say, the middle of the 15th century. Gone were the outdated, primitive huts of a small fledgling village, to be replaced by the more posh stone houses and imposing stone temples of a vibrant, sophisticated city on the move. A system of canals allowed residents to access city blocks amid "floating gardens" known as chinampas, upon which crops and flowers grew. Experts in agricultural and hydraulic engineering, the Aztecs had linked the island of Tenochtitlán to the mainland by causeways, and the marshlands of the lake-shore areas contained the most productive agricultural fields in the New World, able to sustain the city's inhabitants as well as the large Aztec army.
When Hernán Cortés and the Spaniards arrived in the Valley of Mexico in 1519 and looked upon Tenochtitlán, they were amazed by the beauty and size of the sight before them. One of his men compared it to Venice. After pausing to enjoy the view, Cortés and his men then continued toward the city which they would eventually burn to the ground and whose people they would slaughter.
Lost Cities, by Paul G. Bahn, Weidenfeld & Nicolson.