The Alpha Quadrant is the common designation for one-quarter of the Milky Way Galaxy. Its boundary in the region around the Federation is defined by a meridian passing through the galactic core and at least near the Sol system.
Interstellar politics in the Alpha Quadrant in the 24th century were generally dominated by the United Federation of Planets, along with other regional powers including the Klingon Empire, Romulan Star Empire, Cardassian Union, the Tzenkethi, the Talarian Republic, and the Ferengi Alliance, all of which interacted on generally peaceful terms. Members of the Tholian Assembly, Breen Confederacy, and the Xindi remained mostly isolated from the rest of the Alpha Quadrant populations. (Star Trek: Deep Space Nine)
While only about 25% of the quadrant had been sufficiently explored, it was known to contain examples of shocking interstellar beauty and scientific wonder such as the Argolis Cluster, the Arachnid Nebula, and the Badlands. (ENT: "Fusion"; TNG: "I Borg"; DS9: "The Maquis, Part I")
The Bajoran wormhole connected the Bajoran sector in the Alpha Quadrant to a point near the Idran system on the far side of the Gamma Quadrant near Dominion space. The use of this wormhole for exploration and trade by parties from the Alpha Quadrant incited hostility from the Dominion, culminating in the Dominion War. (Star Trek: Deep Space Nine)
In most reference works, apocryphal novels and games, Klingon and Romulan space and parts of the Federation are usually depicted or stated to be located in the Beta Quadrant. This is however inconsistent with dialogue from Star Trek: Voyager and Star Trek: Deep Space Nine, in which all three powers are consistently described as being located in the Alpha Quadrant. The only planet explicitly stated not to be in the Alpha Quadrant was Khitomer in Star Trek VI: The Undiscovered Country. The planet has been established as a Klingon colony in the 2340s in "Sins of the Father" and a planet inside Romulan territory in the 2360s in "Birthright, Part II".
The Star Trek Encyclopedia states that the Federation was spread across the Alpha and Beta Quadrants in order to explain why the USS Enterprise was often the "only ship in the quadrant", though the term quadrant has been often used to refer to smaller segments of the galaxy as well.