Our galaxy, the Milky Way, is also divided into four equal quadrants. They are generally referred to as the Alpha, Beta, Gamma, and Delta quadrants.
The most explored are the Alpha and Beta quadrants, most of which cover the territory of the United Federation of Planets, the Klingon Empire and the Romulan Empire, and other smaller powers such as the Cardassians and the Breen.
The gamma quadrant is probably the least explored. The main power here is the Dominion. The Delta Quadrant is better explored because the USS Voyager was sent here by accident and traveled back to the Alpha Quadrant for seven years, exploring the quadrant. The Borg are probably the biggest power here.