The Ascension Chamber allows you to ascend your dragons to the Hidden World, a process that provides you with Scales or Elusive Scales in return. Similarly to releasing your dragon in exchange for resources, once a dragon is ascended, this action cannot be reverted. You can access the Ascension Chamber by going to Berk's Duties > Ascension or tapping on the cave near Johann's Ship.
In the Ascension Chamber menu, you can select one or more of the same dragon (up to 3 dragons) to ascend. Ascension costs 50 Runes and the amount of Scales/Elusive Scales you obtain will depend on the rarity of the dragon, their level, and the amount that were ascended. Keep in mind that dragons that are currently busy cannot be ascended, they must be on their roost.
You will potentially receive pop ups to verify your choices, as the process is not reversible, so do make sure you trade carefully! The final confirmation message has a checkbox in case you do not wish to view it in the future. Once the Ascension is complete, the dragons you selected for ascension will be removed from your Berk and you will receive the Scales/Elusive Scales.