In Coelho's The Alchemist:
...the Language of the World refers to the oneness of all things: that the [pieces of the] universe [are] tied together.
Santiago (the boy) is on a quest to find treasure in distant Egypt. As he sets out on this journey, with only his dream and some sheep, he learns important truths and receives direction from several people along the way (the gypsy woman, Melchizedek, the crystal merchant, the leader of the caravan, the alchemist, etc., people who already understand the Language of the World). At the beginning, it is his dream of material wealth that motivates him.
Through his experiences, good and bad, Santiago searches for knowledge and meaning. Though he tries to learn through reading, as the Englishman does, the boy recognizes that the books and their words have no meaning for him. He realizes that what he has to learn cannot come from books, but it must come from the world, from the universe.
Having abandoned the books, Santiago begins to recognize signs in nature that have meaning for him: this is the Language of the World. The universe begins clearly to direct the boy's path.
When a person really desires something, all the universe conspires to help that person to realize his dream.
When Santiago reaches the oasis, he meets and falls in love with Fatima. He contemplates turning away from his dream and living out his days with her there. However, he comes to understand that in order to have a meaningful life with Fatima, he must finish his quest and then return to her. Otherwise, he will be forever dissatisfied with the decision he made, much like the crystal merchant.
You must understand that love never keeps a man from pursuing his destiny. If he abandons that pursuit, it's because it wasn't true love... the love that speaks the Language of the World.
If it is true love, Santiago will find his way back to Fatima. The Language of the World is what allows all the things of nature to communicate and work so seamlessly together. It is also what has brought the two together.
Only one who learns and listens to the Language of the World can realizes his or her Personal Legend. Fatima understands this. She knows that if Santiago is to return to her, it will happen if that is his Personal Legend. She already knows the signs of the desert, the Language of the World. So she lets him go.
As the universe conspires to help Santiago realize his dream—his Personal Legend—he faces many hardships, but also learns truths paramount for finding happiness in his life. He recognizes the power he has by being one with nature; he understands that pursuing one's Personal Legend is what brings real treasure. The Language of the World leads him to Fatima in the first place; it draws him away to finish the search for his dream. Ultimately, it directs him back to the oasis, to Fatima.
Santiago finally recognizes that Fatima is his treasure, not something he dreamed was buried in Egypt. And while his original dream eventually comes to pass, it is secondary to the riches he has discovered in his love for the woman he will marry. The Language of the World represents "oneness." This is what Santiago and Fatima discover in each other. And it is through this language that they find each other. The reader finds it again at the end, even though a great distance separates the two:
The wind began to blow again...it brought the scent of a perfume he knew well, and the touch of a kiss...that came from far away...
This is the Language of the World drawing them together once more, as it had done before Santiago ever left the grazing fields with his sheep.