It’s not steam. It’s smoke from wood fired pizza ovens for the turtle men that live there. There was a cartoon documentary about them on tv a few years back.
The New York City steam system includes Con Edison's Steam Operations, a piped steam system which provides steam to large parts of Manhattan. Other smaller systems provide steam to New York University and Columbia University, and many individual buildings in New York City also have their own steam systems. The steam is used to heat and cool buildings and for cleaning and disinfecting. It is the largest such system in the world and has been in operation since 1882.
Some big cities originally heated their buildings by producing steam in one one centralized building and delivering it to large buildings thru pipes underground. The steam you see is from leaking pipes in this antiquated infrastructure. It's a very inefficient method if you ask me. Cities should offer these buildings low interest loans so they can update and be independent but they never take my advice
There’s a lot of things under the streets of New York, many of them cause heat. In order to cool them off the heat is vented outside and the warm moist air meets with the cool dry air and condensates into droplets that we see as steam. Same affect as breathing out on a cold day, you’re not creating steam but it looks that way because the warm moist air from your breath is condensing in the cool dry air.
You know how when rockets take off in Florida there's lots of smoke?
Yeah there's a tunnel that goes from Florida to New York that the smoke goes through to help heat up the New York streets. So anytime you see smoke in New York it's cause a rocket was recently shot up in Florida. Technology Infrastructure is incredible!
Regardless of the truth, I prefer Diane Duane's explanation in the "So, You Want to Be a Wizard" novel, In that all of the steam in the subways are generated by a breed of fire worms. These worms, if left long enough, can grow to the size of a respectable and quite terrifying dragon.
Ah yes, the classic New York fog machine. Turns out it’s not for dramatic effect—just the city’s 19th-century steam system still doing its thing. Who needs modern infrastructure when you’ve got built-in Gotham vibes?
What the other comments aren't mentioning is that, as you've probably learned, poops steam. Put a lot of poops under the ground (i.e. sewers) and that steam has to go somewhere, due to various complex thermodynamic principles that are probably beyond the scope of this question.
They might be smoke testing the system, looking for leaks! Smoke is pumped into water pipe infrastructure and leaks out of potential cracks or undisclosed/illegal sources (such as a company dumping into the sewer system without disclosing it to the city). They do this so they can locate and fix these sources so the water remains uncontaminated by groundwater seepage.