Short answers, pulled from the story.
Mordor is the realm of the Dark Lord Sauron in Tolkien's fictional continent of Middle-earth. It lay to the east of Gondor and the great river Anduin, and to the south of Mirkwood, enclosed on three sides by mountain ranges. Mount Doom, a volcano at its core, was the place where the One Ring was forged and the only place it could be destroyed.
Multiple sources shaped Tolkien's vision of Mordor. He drew on his familiarity with Grendel's unearthly wilderness in the Old English poem Beowulf, on the industrialized Black Country of the West Midlands near his childhood home, and on his experience fighting in the trenches of the Western Front. In a 1960 letter, Tolkien wrote that the Dead Marshes and the approaches to the Morannon owe something to northern France after the Battle of the Somme.
Within Tolkien's fiction, Mordor means Black Land in Sindarin and Land of Shadow in Quenya. Popular sources have linked the name to Old English morðor, meaning mortal sin or murder, but the philologist Helge Fauskanger argued that Tolkien had been using the component elements mor and dor independently for decades before combining them into Mordor.
Mount Doom was represented by two active volcanoes in New Zealand: Mount Ngauruhoe and Mount Ruapehu, both located in Tongariro National Park. The production was not permitted to film the summit of Ngauruhoe because the Maori hold it to be sacred, so some slopes-of-Doom scenes were filmed on Ruapehu instead. In long shots the mountain appears as a large model, a CGI effect, or a combination of both.
Barad-dûr, the One Ring, and Sauron were destroyed on the 25th of March, a traditional Anglo-Saxon date for the crucifixion. Tolkien also set the beginning of the quest to destroy the Ring at Rivendell on the 25th of December, the date of Christmas, giving the entire arc a deliberate liturgical symmetry.
A district in the Mokotów area of Warsaw, Poland, in the neighbourhoods of Sluzewiec and Ksawerow, is commonly known as Mordor. Two nearby streets are named J. R. R. Tolkiena Street and Gandalfa Street in reference to Tolkien's works.