Short answers, pulled from the story.
Rivendell is a direct English translation of the Sindarin word Imladris, both meaning "deep valley." The English name combines "riven" (split or cloven) and "dell" (valley). Within Tolkien's fiction, Rivendell was also called "Karningul" in Westron, the Common Tongue of Middle-earth.
Tolkien based the Rivendell valley on Lauterbrunnen in Switzerland, where he went hiking in 1911. He stated directly that the journey from Rivendell across the Misty Mountains, including the glissade of Bilbo and the dwarves down slithering stones into the pine woods, was based on those Swiss adventures.
The Fellowship sets out from Rivendell on the 25th of December, the date of Christmas, and the One Ring is destroyed on the 25th of March, the date in Anglo-Saxon tradition for the Crucifixion. The scholar Tom Shippey notes that Tolkien, a devout Christian, was extremely careful with these dates, though almost no readers notice them.
Scholars have compared Rivendell to the Celtic Otherworld known in Irish as Tir na nOg. Both are hard to find; both require the traveler to cross a river as a spiritual threshold; and both offer the weary visitor Elvish hospitality and a sense of timelessness. The descent into the valley also parallels Celtic tales of entry into the underground realm of the Tuatha De Danann.
Rivendell was filmed at Kaitoke Regional Park in New Zealand for Peter Jackson's 2001 film The Fellowship of the Ring. The waterfalls seen in the film were added with computer-generated imagery rather than filmed on location.
In 1968, a commune called Maos Lyst was founded on the island of Zealand in Denmark, and its members replaced their family surnames with Klovedal, the Danish word for Rivendell. Several of those commune members later became well-known cultural personalities in Denmark.