How and why did the Aztec settle where they did?

As the legend has it the empire was formed in a swampy place where they seen an eagle perched on a cactus eating a snake. This is what the Aztecs claimed they saw while entering the new land. They began building and constructing their capital city, and by the year 1325 their capital city was finished. They called it Tenochtitlan, meaning "Place of the Prickly Pear Cactus".