The Alpha Quadrant is one of the four quadrants of the Milky Way Galaxy. It's inhabitants include the United Federation of Planets, the Cardassian Union, and parts of the Klingon and Romulan Star Empires.
A wormhole was found near planet Bajor and space stattion Deep Space 9 that connected the area with the Gamma Quadrant, the discovery of which eventaully led to the Dominion War.