The Dominion is an interstellar empire, located in the Gamma Quadrant. It was founded and led by the Founders, who over some 2000 years conquered countless worlds across the Gamma quadrant, maintaining order with their genetically modified minions and armies; the Vorta and the Jem'Hadar.
The Dominion made first contact with the Federation when they briefly captured Commander Benjamin Sisko, commanding officer of Deep Space Nine, his son Jake Sisko, Jake's best friend Nog and Nog's uncle Quark in the year 2370 on a planet in the Gamma quadrant (DS9 episode: The Jem'Hadar).
Tensions grew between the Dominion and the major Alpha Quadrant powers, however by 2373, Gul Skrain Dukat of the Cardassian Union managed to strike a deal with the Dominion and the two governments formed an alliance. (DS9 episode: By Inferno's Light).
The war raged for two years with the Dominion gradually becoming more oppressive over their Cardassian hosts in the Alpha Quadrant whilst the Federation lead an alliance including the Klingons and Romulans to fight the Dominion threat.
A peace treaty was drawn up between the Dominion and the major powers of the Alpha Quadrant and the Dominion retreated back into the Gamma Quadrant.
Following the war relations between the Dominion and the Alpha Quadrant remained mostly civil with the Dominion allowing Federation starships into the Gamma quadrant on exploration missions and the Founder Odo sending a Jem’Hadar envoy named Taran'atar to Deep Space Nine to gain the Dominion a greater understanding of the Alpha Quadrant’s cultures. (DS9 novel: Avatar)