A map of the Milky Way Galaxy
The Norma Arm is a collection of stars, planets, nebulae, and other spatial objects that form one of many curved "arms" outshooting from the center of the Milky Way Galaxy.
The Norma arm seems to extend from the galactic core at the Alpha Quadrant-Beta Quadrant border, through the center of the Beta Quadrant, and ending a little into the Delta Quadrant.
The Norma Arm was shown on a computer panel in Astrometrics on USS Voyager during the later years of its seven-year journey in the Delta Quadrant. (VOY: "Endgame" display graphic)
The graphic is also shown (in legible detail) in Geoffrey Mandel's Star Trek: Star Charts. In current astronomy, the Norma Arm is also known as the "Cygnus Arm."