It was, in fact, an aqueduct, though I don't see how that would be surprising. A city the size of Tenochtitlan, even one in the middle of a lake, is going to need an additional source of fresh water.

The aqueduct ran from the springs of Chapultepec (yes, where modern day Chapultepec Park is) into the heart of Tenochtitlan. The details of the pre-Hispanic construction are a little hazy (understandable, given its destruction and that it was probably rebuilt at least once before then), but a raised earthwork with packed clay channels is the consensus. Removable wooden sections were also used to allow ship traffic through the causeways the aqueduct ran along. This schematic should paint a better picture than my words. Another oft cited, but more poorly documented feature is a dual-channel system that allowed one channel to continue to flow even as maintanence/cleaning was performed on the other.

In the late 1400s/early 1500s another main aqueduct was built, again following the causeways, from Coyoacan. Famously, it was blamed for contributing to the flooding of Tenochtitlan, though this is a city wherein floods were to be expected. Aside from these main aqueducts, there were smaller works scattered throughout the Basin of Mexico to redirect water on a more local scale. Like with all things Aztec, the archaeology of these has been somewhat stymied by the fact that the metropolis of Mexico City (née Tenochtitlan) sits atop the area. Portions of the Colonial-era rebuilt Chapultepec Aqueduct, however, still exist.

As for sanitation, the Aztec system was to have public collection points for excrement, which would then be carted off to be used as fertilizer (solid waste) or in tanning (liquid waste). This is in addition to the public servants who kept the street clean. Harvey (1981) is a seminal paper on the topic which still acts as good introduction/overview.