Betazed was an important member world of the United Federation of Planets and its society had matriarchal elements. The Betazed Federation ambassador during the 2360s and '70s was Lwaxana Troi, daughter of the Fifth House, holder of the Sacred Chalice of Rixx, heir to the Holy Rings of Betazed. (TNG: "Angel One", "Manhunt", DS9: "The Forsaken") Betazed depended on Starfleet for protection as its planetary defenses, in the opinion of Captain Benjamin Sisko, the CO of Deep Space 9, were ...obsolete and undermanned. (DS9: "In the Pale Moonlight")
During the Dominion War in 2374, Betazed was occupied by Dominion invasion forces. The Federation Tenth Fleet had been assigned to defend Betazed and its outlying colonies, but was caught out of position on a training exercise. As a result, Betazed fell to the Dominion within ten hours. Once Betazed had been captured, other worlds nearby, including Vulcan, Tellar, Alpha Centauri, and Andor were at risk of Dominion invasion. (DS9: "In the Pale Moonlight")
Dominion forces occupied the surface of the planet. Towards the end of the year, in a single month, the Second Fleet attempted on three separate occasions to hit those forces, but was repulsed each time. After each strike, the Dominion was able to send in reinforcements and refortified their positions on the planet. (DS9: "The Sound of Her Voice")
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According to the script for "Q-Less", the pronunciation for Betazed was "BAY-tuh-zed". 
According to Star Trek: Star Charts (p. 33), Betazed was the fifth planet in the Betazed (Beta Zeta) system. The official name of the government was the Fifth House of Betazed, which governed this planet from the capital city of Rixx. Betazed was admitted into the United Federation of Planets in 2273. As reported in the census of 2370, the planet was populated with 1.3 billion Betazoids living there. Betazoids had been warp-capable since antiquity. Major attractions on this world included Lake Cataria, Janaran Falls, and the University of Betazed. The system was named by the 21st century Human John Burke, chief astronomer of the Royal Academy.
According to Star Trek: Star Charts (pp. 36 & 48) and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), the Betazed (Beta Zeta) system was located in the Alpha Quadrant. The primary was a G-class star. In October 2374, the Dominion won the Battle of Betazed and claimed the system. (Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography" p. 41; "The Dominion War: Strategy and Battles, 2373-75") placed this event in September 2375.)