The Dark Fountains are power sources that give the Dark World form. Only the Fountain of Darkness is supposed to be standing, but according to King and Queen, the Knight has been opening new Fountains. The Prophecy says that the three Heroes of Light are destined to close the Fountains to restore balance to Light and Dark.
Fountain of Darkness
The Fountain of Darkness towers above Castle Town, visible at or near the castle Ralsei, the Prince of Darkness, lives in. In Ralsei's prophecy, he states that the Fountain of Darkness "gives this land form." Darkners who leave the Dark World that they originate from quickly grow weak, before turning into stone statues. The only exception to this effect is the Dark World shaped by the Fountain of Darkness. As Ralsei puts it, the Fountain of Darkness is "made of pure darkness", allowing all Darkners to persist.
The Eastern Fountain is the second Dark Fountain that Ralsei mentions in his prophecy, created by the Knight and threatening to upset the balance of Light and Dark. Reflecting the school's unused classroom, it stands at King's Card Castle, and is closed using the power of Kris's human SOUL at the end of Chapter 1.
The Library Fountain is the third Dark Fountain encountered in Deltarune, and the primary fountain of Chapter 2. The fountain was opened in the library, and created an electric-themed Dark World ruled by Queen. Despite Queen's initial efforts to the contrary, the fountain was closed by Kris's human SOUL at the end of Chapter 2.
In the final moments of Chapter 2, Kris, under possession, uses a knife to open a Dark Fountain in the middle of the living room while Toriel and Susie are sleeping.