From Star Trek: Theurgy Wiki
The Alpha Quadrant was the common designation for one-quarter of the Milky Way Galaxy. It was adjacent to the Beta Quadrant and the Gamma Quadrant. One-quarter of the galactic core was located in this quadrant.
In late 24th century interstellar politics and diplomacy, the four great powers in the Alpha Quadrant were the United Federation of Planets, the Klingon Empire, the Romulan Star Empire, and the Cardassian Union. Other powers at the time were divided into two groups. The mercantile powers, like the Ferengi Alliance, traded with the great powers. The isolationist powers, like the Breen Confederacy and the Tholian Assembly, defended their territory aggressively and, would on occasion, battle with other powers. By the late 23rd century, the Alpha Quadrant still remained largely unexplored by the United Federation of Planets.
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. Source: Memory Alpha