The climax occurs when Santiago and the alchemist are captured by Arab tribesmen who accuse them of being spies. On further questioning, the alchemist tells the Arabs that Santiago is an alchemist who can destroy the military camp by summoning the wind if he chooses to. The chief demands to see such a preposterous claim fully demonstrated, and the alchemist asks for three days for Santiago to accomplish this feat.
Santiago is frantic because he does not know how to turn himself into the wind. However, in due time, he comes to learn the truth about the wind and personal miracles. One of the most important passages to the climax is:
"This is why alchemy exists," the boy said. "So that everyone will search for his treasure, find it, and then want to be better than he was in his former life. Lead will play its role until the world has no further need for lead; and then lead will have to turn itself into gold."
Why is this passage important?
This passage encapsulates the main theme of The Alchemist. Santiago comes to understand what pursuing one's Personal Legend really means. It means harnessing all the gifts of the world and the gifts of love to become a better person and to accomplish feats of excellence that in turn benefit the world. Santiago learns that this is how we return love to those whose love motivates us to greatness.
We were all made by the same hand, and we have the same soul. I want to be like you, able to reach every corner of the world, cross the seas, blow away the sands that cover my treasure, and carry the voice of the woman that I love.
Yes, that's what love is. It's what makes the game become the falcon, the falcon become man, and man, in his turn, the desert. It's what turns lead into gold, and makes the gold return to the earth.
Hope this helps! Thanks for the question.