As of New Year's Eve, all underground New York City subway stations offer passengers and others in the stations free WiFi, delivering on a promise made early in 2016 by New York State Governor, Andrew Cuomo, that the convenience would be available by year's end.
WiFi rollout in New York has been a long process - beginning with the service going live at some major stations over five years ago - and its completion marks a significant accomplishment. Many New York City subway stations are deep underground where cellular signals are faint or non-existent, so, until the deployment of in-station WiFi, passengers were cut off from modern communications even when waiting for trains. Besides being an inconvenience, this meant that passengers who needed to "send a quick email" before traveling would either have to do so from outside stations and miss trains, or take taxis.
Free WiFi is a great, valuable convenience. It is important to understand, however, that using public WiFi creates several significant security risks, so before using WiFi in New York City subway stations or anywhere else, be sure to check out the article How to Safely Use Public Wi-Fi.
In addition to WiFi, cellular service is also available in some subway stations; those presently lacking the convenience are expected to be equipped over the course of 2017.
Besides offering convenience, WiFi and cellular service also improve passenger safety - would-be criminals know that people waiting on platforms can contact police, send images, and even livestream.
WiFi and cellular service are not presently available on trains traveling between stations; early tests of technology to deliver such capabilities began this past summer, but no rollout plans have been announced; if in-transit WiFi is not deployed en masse sooner, it should certainly be available on next generation subway trains that are expected to arrive on tracks for testing in 2020.
Instructions are available here on how to connect to free public WiFi in New York City subway stations.