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)
According to scenic artist Geoffrey Mandel's book, Star Trek: Star Charts, as well as the Star Trek Encyclopedia and the video game Star Trek Online, the Alpha Quadrant was not home to the more recognizable species like the Vulcans, Klingons and Romulans – rather these species resided in the Beta Quadrant. Strictly speaking this is inconsistent with the TV series, which consistently describe these territories as belonging to the Alpha Quadrant and rarely mention the Beta Quadrant at all. This may be reconciled by treating use of the term "Alpha Quadrant" as a colloquialism for the Federation and its neighbors (in other words, anywhere starships can go without being whisked across the galaxy via extraordinary means), much like the West is a colloquialism for European and North American cultures. However, Star Trek: Star Charts and Star Trek Online are not a canon sources.
The Star Trek Encyclopedia states that the Federation was spread across the Alpha and Beta Quadrants in order to explain why the Enterprise was often the "only ship in the quadrant" (for example, the Beta Quadrant). However, this could also be explained by assuming that the "quadrant" in question is a different, smaller unit of measure, as in the Morgana Quadrant or Quadrant 448.