The Demon's Falls are a waterfall in Nohr that actively spews fire. This is caused by a massive reservoir of oil that had mixed with the water. At some point, hundreds of years ago, the river was set aflame, making people of Nohr avoid that area. While normally impassable, wielders of the Dragon Vein ability are able to halt the lava via a number of special statues between the numerous flows. Unbeknownst to most people, there is a secret passage from this location that leads directly to Windmire, the Nohrian capital city, which is suggested to have been built by the Rainbow Sage.
In Chapter 21 of Birthright, Ryoma mentions that the route they were currently taking would take them at least two days to reach Nohr. This worries him because of a message that Yukimura sent him via a Pegasus Knight that was weeks old, giving the status of the bordering back at Hoshido. However, Takumi tells Ryoma that there was another pathway on the hand drawn map the Rainbow Sage gave to them earlier before they boarded the ship. He then points to an area on the map, saying that there was an area that was faintly written and read, "Demon's Fall". As he mentions the name, it causes Ryoma to make Takumi show him immediately where it was; this was because he thought of Demon's Falls to be a fairytale of sorts.
When they get there, Ryoma comments on how real Demon's Falls is now that he's seen it in person. Jakob then explains to him how it was set aflame. Apparently, a massive reservoir of oil that was mixed in with the water was set aflame by some unknown force at one point, hundreds of years ago. There had been theories that had tried to explain how it was caught on fire, with one of those theories being a stray lightning bolt striking the river.