The Archanis sector was a region of space near the Federation-Klingon border. The sector was originally claimed by the Klingon Empire, but was relinquished to the United Federation of Planets in the mid-23rd century. It contained the planet Archanis IV, as well as a number of Federation starbases and outposts. (DS9: "Broken Link")
In late 2372, Chancellor Gowron demanded that the Federation relinquish the sector to the Klingons, at the urging of whom he believed to be General Martok. (DS9: "Broken Link") In reality, this Martok was a Changeling who had replaced the real Martok over a year earlier. A Klingon task force took the sector shortly after, starting the Federation-Klingon War. (DS9: "Apocalypse Rising")
Background information Edit
Kira Nerys stated that the Klingons had given up their claim "one hundred years" before 2372. The Star Trek Encyclopedia, (3rd ed., p. 19) says the Klingons relinquished the Archanis IV (though remaining silent about the sector) in 2262, which would be exactly 110 years before Kira's statement. However, the vague quote also puts it roughly around the time of the 2267 Treaty of Organia, which involved provisions for the changing hands of planets.