NYSE - New York Stock Exchange
The NYSE is the oldest stock exchange in the United States and one of the biggest exchanges in the world. When news anchors show something happening in the economy, they almost always flash an image of the floor of the NYSE.
NASDAQ and electronic trading networks have meant that the NYSE is less important than it used to be... but don't tell them that; they get very touchy about it.
Companies can list their shares on the NYSE if they meet SEC standards and go through a whole process of getting listed.