One of the galaxy's four quadrants, home to much of the United Federation of Planets as well as the Cardassians, the Ferengi and many other powers.
The Alpha Quadrant is one of the four quadrants into which Starfleet divides the Milky Way galaxy. It covers one quarter of the galaxy and contains a large part of the United Federation of Planets. Earth sits near its border with the Beta Quadrant, and it is also home to the Cardassian Union, the Ferengi Alliance, Bajor, the Breen and many other species.
Much of Star Trek takes place in the Alpha Quadrant, from the Federation's border conflicts to the Bajoran Wormhole that links it to the Gamma Quadrant. When the Dominion arrived through the wormhole in the 2370s, its leaders aimed to conquer the region, and the Dominion War pitted the Federation, the Klingons and the Romulans against the Dominion and the Cardassians for control of it.
The term is often used loosely to mean the familiar part of the galaxy, even when the Beta Quadrant powers are included. For the crew of Voyager, stranded far away in the Delta Quadrant, the Alpha Quadrant stood for home, and getting back to it was their constant goal.