This mountain is a sacred place in Prythian as it is believed to be the point from which the rest of the world was created.
When Feyre Archeron is at the Spring Court she sees a map that tells the history of the world. In it, the Cauldron dumps its content and comes into contact with the surface and a mountain is formed. Then it forms the other territories to the form the world currently has, and it is for that reason that this mountain located in the Prythian area known as the Middle is sacred to faeries and is considered neutral land.
After Amarantha proclaims herself High Queen of Prythian, she takes inspiration from the Hewn City or Court of Nightmares of the Night Court and builds a palace under this mountain where she founds her court and holds the residents of the other Prythian courts captive except the Spring Court and those whose High Lords swore allegiance to her.
After the forty-nine year term she gives Tamlin, the High Lord of the Spring Court to find a mortal girl who hates faeries but loves him has passed she takes the entire Spring Court to Under the Mountain and makes the residents of the other courts go there too.
After Feyre Archeron, the human who loves Tamlin appears there and successfully passes the three trials imposed by Amarantha and solves the riddle too, the High Lords regain their full powers and Tamlin kills her. In this way the palace of Under the Mountain is destroyed and the mountain is no longer used as a neutral place as in the past due to memories of Amarantha's reign of terror over Prythian.