The Elven forest kingdom that rests between the Misty Mountains and the Anduin river a short distance south-east of Khazad-dûm.
Founded by Silvan elves sometime prior to the First Age (it is assumed). Later, elves living in Lothlórien became known as the Galadhrim, after Galadriel, one of its rulers. Strangely, though, neither she nor her mate, Celeborn, were Silvan elves; she was of the Noldor, he was of the Sindar.
Lórien was ruled by Malgalad during the Second Age (he died at the end of the Second Age, during the War of the Last Alliance; the exact length of his reign is unspecified). After that Amroth was king for many years until he was lost at sea while searching for Nimrodel, on the cusp of the beginning of the third millennium of the Third Age, at which point Celeborn and Galadriel became the Lord and Lady of Lórien, respectively. They ruled for approximately one thousand years, until shortly after the War of the Ring (in the Fourth Age), at which point they separated (perhaps temporarily) when Galadriel sailed west to Valinor, and Celeborn left the area to travel in Middle-earth for an undetermined amount of time (his final fate is never established).
Celeborn and Galadriel's "capital city" was known as Caras Galadhon ("Fortress of Trees").
The literal meaning of Lothlórien is "Lórien of the Blossom," referring to the land of Lórien in Valinor. It is also known as Dwimordene among the Rohirrim, and prior to Celeborn and Galadriel's arrival, in the old days, was called Lindórinand (among other names). Though the name is most properly "Lórien," the most commonly used name is probably Lothlórien.
By the first century of the Fourth Age, all the elves dwelling at Lothlórien had sailed west or moved elsewhere, and it was an empty land. After the death of Aragorn II Elessar, his widow Arwen traveled there to die in grief.
(see J.R.R. Tolkien and read The Lord of the Rings and The Silmarillion)