The Forgotten Realms is a fictional setting created by author and game designer Ed Greenwood for the Dungeons & Dragons (D&D) role-playing game. It is based very loosely on Europe in the Middle Ages, with a fair number of large and cosmopolitan cities scattered throughout the realms, some as capitals of larger kingdoms but many as independent city-states forging their own destiny. Most action in the Forgotten Realms takes place on the supercontinent Faerûn of the planet Toril, and many publications regarding the Forgotten Realms are really specifically about Faerûn. As this setting has become the official setting endorsed by Wizards of the Coast, it is the only setting permitted for the official campaigns and most premium modules (the first batch of premium modules—Witch's Wake, ShadowGuard, and Kingmaker—was not subject to this restriction).
Originally designed as Greenwood's personal campaign, the Forgotten Realms became the setting most popular with D&D gamers in the 1990s, following a long series of articles detailing the setting in Dragon magazine. Its fame has been boosted by dozens of novels (including the exploits of the drow Drizzt Do'Urden) and numerous computer role-playing games, including Pool of Radiance, Unlimited Adventures, Baldur's Gate, Icewind Dale, and Neverwinter Nights).
As with standard D&D, many planes of existence make up the cosmos of the Forgotten Realms, with the primary location (in this case, the plane containing Toril) called the Prime Material Plane. This cosmology is completely enclosed and separate from the "planar wheel" of standard D&D, though (aside from the inclusion of Sigil, which connects all worlds).
The Forgotten Realms has several polytheistic pantheons, and deities are an integral part of life in Faerûn. Deities interact with mortals, answer prayers, and have personal agendas. In the history of Forgotten Realms, some mortals rose to godhood. They have many servants on the Material Plane, in the form of worshipers, clerics, paladins, proxies, and the Chosen. The Chosen are mortal worshipers who have received a portion of their deities' power, acting as mortal representatives of their deities. The most famous are the Chosen of Mystra, among whom is Elminster, the Sage of Shadowdale.
Above all other deities is Ao the Overlord. Ao does not sanction worshippers and distances himself from mortals. He is single-handedly responsible for the Time of Troubles, or Godswar, as seen in The Avatar Trilogy of books.
Forgotten Realms wiki - A work in progress wiki to detail the Forgotten Realms Campaign Setting.