Mellon is the Elvish word that opens the door to the Mines of Moria.
The Doors of Durin stand on the western entrance to Moria, also called Khazad-dûm. Their inscription includes the instruction to speak the word “friend” in the language of the Elves. Gandalf eventually realizes that the required word is “mellon,” a Sindarin word meaning “friend.”
The doors were made by the Dwarf Narvi and featured designs by Celebrimbor, an Elf of Eregion. Their cooperation reflects the former friendship between the Dwarves of Moria and the Elves of Eregion. The doors are magical in appearance but function through a password rather than brute force.
Readers sometimes remember “mellon” as a general Elvish greeting, but in this scene it is specifically the password connected with the Doors of Durin. The word is Sindarin, not Quenya. Tolkien’s use of a short linguistic puzzle also makes the scene an example of how language, history, and plot are tightly connected in The Lord of the Rings.