Jaywalking is generally defined as crossing the street recklessly, ignoring red lights etc. etc.
In New York, jaywalking is part of blending in: You cross the street when you have to and deem it reasonably safe to do so. Otherwise you may just be in the way of someone in a hurry (Rule #1, remember?). Pedestrian traffic lights are commonly understood as recommendations. They may or may not indicate that you are allowed to walk, but don’t really promise any real safety. Watch out for cars taking a turn. They may just ignore you – take it from someone who almost got run over twice.
PLEASE NOTE: While jaywalking is technically a misdemeanor in NYC, yet nobody will really write you a ticket for it (NYC police officers have better things to do), it comes with a hefty fine in other American cities (LA, for example). So, check the local regulations and customs.