Alphinaud asks you to accompany him to the Rising Stones for the task that he must do.
This quest is available if you have completed the quest Awakening in Ul'dah.
Starting the Quest
Talk to Alphinaud at the Chamber of Rule in Ul'dah to begin the quest. There will be a cutscene.
Enter the Rising Stones
Go to Revenant's Toll in Mor Dhona and go into the building south of the Aetheryte, and enter the Rising Stones. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.
Speak with Alphinaud
Talk to Alphinaud to complete the quest.
Next Main Scenario Quest
After you complete the quest, you will need to be at least level 55 to proceed to the next quest. After you reach level 55, talk to Alphinaud to accept the next quest: Ready to Fly.