The New York Times is the biggest newspaper in New York City. It may also mean the time zone in New York City, which is -5 UTC right now.

New York City is a prominent US city that everyone knows about. It is in the Eastern Time Zone, meaning NY time is another word for Eastern Standard Time for most people along the eastern seaboard. For some people, NYC is a major hub for most industries so many people are going to need the specific time for the city also.

NY= New York.... so New York time. With an -s, it would mean New York Times, which is a famous newspaper, from New York City, or NYC