River Song's World was an alternate timeline - described by the Eleventh Doctor as "another reality" and River Song as a "world that never was" - created by River Song when she refused to kill the Eleventh Doctor, interfering with a fixed point in time. Time itself began to collapse and all of Earth's history occurred simultaneously within a bubble of time, with the rest of the universe still turning outside.
River Song prevented the "death" of the Eleventh Doctor, which occurred on 22 April 2011 at Lake Silencio, Utah. River, knowing that Madame Kovarian had forced her to assassinate the Doctor, drained her suit of power.
In this alternate timeline, the War of the Roses had entered its second year, pterodactyls flew through the air and Winston Churchill was the Emperor of the Holy Roman Empire and travelled on his personal mammoth. Charles Dickens was also in the middle of writing A Christmas Carol and was being interviewed by the BBC. River, with the aid of President Kennedy and Cleopatra, had transformed one of the Pyramids of Giza into Area 52. Earth was also experiencing the side effects of what were believed to be solar flares, but were actually messages from the original timeline, responding to a distress call sent out by River.
Churchill sensed that something was wrong because the time and date never changed. He had the Doctor, who was his soothsayer, brought to him and demanded he explain why the time never changed. After the Doctor had explained how this timeline had been created, Churchill and he were attacked by Silents, only to be rescued by soldiers led by the alternate Amy Pond. She remembered certain things about her travels with the Doctor in the original timeline, but initially couldn't remember that Rory Williams (one of her soldiers) was her husband.
This alternate timeline was negated when the Doctor convinced River Song to make physical contact with him in the form of a kiss. Because she and the Doctor were the opposite poles of the disruption in time, their touching caused time to be returned to its original state, where River "killed" the Doctor. (TV: The Wedding of River Song)
A Dalek continuity bomb revealed another version of the timeline where the Eleventh Doctor chose not to save the universe after River refused to kill him. The Doctor and River married in this timeline and lived a domestic lifestyle, even as the rest of the universe would inevitably collapse around them. The Tenth, Eleventh and Twelfth Doctors briefly visited this reality to collect the equipment they needed to defeat an alternate version of the Twelfth Doctor. (COMIC: Four Doctors)