A tenement is a run-down apartment building. The tenements in Old New York were barely safe enough to live in — fire hazards, no air circulation, and no bathrooms, either.
When different immigrant groups first came to the United States in the 1800s, they didn't have much money and would often end up living in close quarters with many people in a small apartment, or tenement. These buildings were notorious for catching fire and collapsing. In 1901, New York City passed a law that said all tenement apartments had to have running water — ah, indoor plumbing! — and required that each room have a window.
