Alchemy has become synonymous with transformation. Historically, an alchemist was someone that could transform ordinary lead into gold. Just to be clear, that is not possible. Both gold and lead are two different and distinct pure elements. No chemical reaction will change one into the other. Regardless, alchemy gives the perception that something of almost no value can be changed into something of great value and importance.
That is exactly what Santiago went through. He began the story as a lowly sheep herder. He did have a great desire to travel the world and see great things, but he didn't aspire to be much more than what he was.
But ever since he had been a child, he had wanted to know the world, and this was much more important to him than knowing God and learning about man's sins.
However, by the end of the story, he is a very different man. He is strong and confident in his abilities, and he makes decisions of his own. Not only that, but he has gained the ability to commune with the "Soul of the World." Lastly, he also, at one point, physically transforms himself. That sounds a lot like alchemy to me.
An alchemist is supposedly able to transform lead (or any other ordinary metal) into gold. While there is a character in the novel that is an alchemist, I think Paulo Coelho is referring to how the boy Santiago is able to transform his ordinary life into "gold". The boy goes from being an ordinary sheep herder to one who lives out his Personal Legend. The prize was actually not the treasure he found at the end, but the real treasure he found within his heart that made his life extraordinary. By living his Personal Legend, Santiago is like the alchemist who changes the ordinary into gold.