The story of Tiberius's two sons, one a poet and the other a soldier, is narrated to Santiago by the Alchemist at the Coptic monastery. In a dream an angel told Tiberius that one of his two sons would become famous and his 'words' would become famousand Tiberius presumed it would be his poet son. When he dies, Tiberius thanks the angel for telling him thatb his son's poetry would live after him and be famous; but the angel surprisingly contradicts him, and says that his poet son's poetry was forgotten, it was the other one, the soldier son, who achieved fame and immortality-- simply by believing in the 'Son of Man' (i.e. a reference to Jesus Christ) and by having faith in his power/ability to heal the ailing. Thus, this son's words addressed to Christ, seeking help for his servant, became famous in history.
In a basic sense, this is a simple moral story told by the Alchemist to his disciple Santiago where he is warning/advising him not to follow just appearances or what seems 'obvious' but to seek the real meaning of things.
On a deeper, spiritual/mystic level (and ''The Alchemist'' is ultimately a mystic work) we have here a master, a seer , addressing a disciple with a profound truth about the nature of the universe and of existence and being i.e. that is, (a) the Truth often manifests itself in unexpected ways and places (b) things arent what they always seem or appear but they have an 'inner meaning' which is often hidden from us until the time when it is fated to be revealed (c) faith and belief are central to achieveing one's true life goals, and not necessarily worldy success and such. This story is related to Santiago as a 'lesson' by his master, at a crucial time, when Santiago is on his way to the pyramids to seek his 'treasure' -- but where lies his 'real' treasure? This is also implied heer.