The titular spire is actually a tall tower topped with an onion dome. In middle of this tower is a giant black obelisk that dangles like a chandelier and is device that dreams are realized. I think it can tell the future too. Elika says that when she was a child she would sleep on the roof.
The center of the spire is an elevator that you must hand-crank to get to the top. When you get half-way up, the princess again gets stuck in the Concubine's corruption trap and again the Concubine tricks the prince into swinging at her phantasms. After chasing the Concubine a bit, the princess is free so grab the elevator handle and continue up to the next floor.
As you climb along the walls of the next level, the concubine taunts and says that she can make dreams true, and she offers travel for Elika or implied oral sex for the Prince.
After you get to the top, you face the Concubine:The Concubine:
With her defeat, the Prince and Elika tease each other about the Prince's crush on the Concubine. (see comments on drag queen###LINK###)
After the fertile ground has been restored you must continue on down the outside of the tower. From the top, look for a small bump outward (Elika's navigation ball will point to it too) and lower yourself over the edge, and Beyonce-robo-glove your way down the side of the tower. Look for the faint path of scratch marks implying that a lot of people use this same method to descending the tower.