The Sewer is a modern way to sustain a bigger Population in a city. It comes at a moment when most old cities in an empire have reached or exceeded their Housing cap, and their growth has been severely crippled. The other late game Housing tool - the Neighborhood - is a district, and as such takes up space around the city, whereas the Sewer doesn't.
Put enough people and animals in one place, pave over the streets, let it rain … and the need for a sewage system becomes evident. At least it did to the Indians; the oldest covered sewers uncovered by archaeologists have been found in the ruins of the Indus Valley civilization. Where to put the runoff from the waste water and sewage was always a problem; the great Cloaca Maxima in ancient Rome, considered an engineering marvel, emptied into the Tiber River (hopefully, downriver from where the city’s drinking water was acquired). In many places, a natural waterway was covered over and served as the sewer system; London’s River Fleet is one such. With the advent of the Industrial Revolution, and the explosive growth of cities, during the early 19th Century many civil engineers urged the construction of integrated, purposeful water and sewer systems; the “Great Stink” of 1858 in London resulted in the first “modern” sewer system, funded by Parliament, and became the basis for all the sewage innovations since.
The Sewer is a required feature for the achievement "Pizza Party!", which gives tribute to Teenage Mutant Ninja Turtles. Also required are the Great People Leonardo Da Vinci (Great Engineer), Michelangelo and Donatello (Great Artists), along with the city of New York.