NYSE stands for the New York Stock Exchange.  This is the oldest stock exchange in the US.

The NYSE is closely related to the various regional exchanges.  All listed stocks on the various regional exchanges could be traded on any of the regional exchanges, and they were all traded by similar methods.  With the introduction of NYSE Direct Plus and other measures, the distinctions between the NYSE and the NASDAQ are slowly disappearing.

The NYSE still uses a specialist, a single hub for all orders.  This makes the biggest difference at the open, when the specialist has the most information about and control over the stock price.