The Delta Quadrant is a term designating a quarter of the Milky Way Galaxy. The Federation defined its boundary by a meridian that passed through the galactic core and the Sol system, and a second meridian 90° perpendicular at the galactic core.
In 2371, the USS Voyager was transported to the Delta Quadrant and was faced with a 70,000 light year journey back to the Federation. After a seven year journey Voyager returned to Earth bringing with it a vast knowledge of the regions of the Delta Quadrant it traveled through. (Star Trek: Voyager)