I am assuming that the question is in reference to Mary Shelley's Frankenstein.
Frankenstein opens with Robert Walton's letter from St. Petersburgh, Russia, to his sister in England for several reasons, both literary and psychological. There are many examples of works in English and European literaturethat begin with a tale within a tale: The Rime of the Ancient Mariner and Wuthering Heights readily come to mind. But whereas those are tale-within-a-tale narratives, Frankenstein is actually a letter written by a brother to his sister.
In order to understand why Shelly chose to situate the letter at the beginning, let me refer you to a very interesting book by the late Edward Said called Beginnings (1985). In this book, Said analyzes the beginnings of several types of literary and journalitic works and comes up with the hypothesis that, in the begiining of a work, a microcosm of the whole work is embedded. This is why, writes Said, perhaps with tongue in cheek, authors write the introduction to their works last!
Applying Said's theory to the letter with which Frankenstein opens, we find that this letter contains, not only the moral of the story of Frankenstein, but, in fact, parts of the letter signifies and even foreshadows what is to follow in the story proper.
To begin with there is that thirst for adventure and knowledge; an indomitable desire to know everything there is to know, to create that ultimate phenomenon that will answer all questions humans are capable of asking.
But beware: desire for knowledge caused the angels to fall!
The witnessing of the man-made monster is of course, quite literally a foreshadowing of the story, a near cinematic image before the days of the cinema! But it is more than that.
To Christian readers, this part of Walton's letter can be understood as the ultimate perversion of human desire -- the creation of a deformed creature because only God makes human beings in His own image. Not only, is the monster ugly, he is dangerous -- for he has a human brain to go with his super human strength.
Finally, the story. The letter ends with the announcement of the story, in the conventional tale-within-a-tale that sets up the actual story of Frankenstein as a prologue would a play.
I hope this answers your question.
First, the technique of using letters at the start of a novel of this time period serves as an authenticating device, suggesting to the skeptical reader that the seemingly wondrous tale about to be told is not mere fiction. The letters provide a sense of realism to a story that will require the suspension of the reader's disbelief.
The letters that begin Shelley's novel Frankenstein, or, The Modern Prometheus, serve to highlight and parallel for the reader some of the key themes of the novel, including the dangerous quest for knowledge beyond human purview and the consequences of alienating oneself from one's community. Robert Walton, who writes the letters to his loving sister, is on a journey to the North Pole in the hopes of discovering how the magnetic forces in the universe work. Not only is his journey fueled by his insatiable curiosity and the thirst for knowledge, but, more significantly, it is fueled by his desire for glory. He wishes to "accomplish some great purpose " and prefers "glory to every enticement that wealth placed in his path" (Shelley 15). In other words, once he discovers how the magnetic forces work, he hopes to control them to better mankind. To achieve this goal, he has isolated himself from the loving company of his sister. He acutely feels the loneliness of his choice and "desires the company" of someone with whom to share either his joy or disappointment (17).
Walton's tale told in his letters is the first of three tales told in the novel. When Walton rescues the almost-dead Victor Frankenstein and brings him on board the ship, the second of the three tales begins. After Walton shares his story of the purpose of his journey, Victor is compelled to narrate his story as a cautionary tale to his new friend. Victor's tale is another story of a quest for knowledge, a quest for glory, and a quest for mastery of nature's and God's mysteries.
Finally, the letters parallel the monster's quest for knowledge, the acute loneliness that he feels, his alienation from mankind, and his desire for human companionship. He, too, must tell his tale.
As you read Walton's letters and then read Victor's and the monster's stories, look for similarities in phrasing and language. You will find, repeatedly, lines that parallel each other in wording, tone, and theme. In fact, if you were to erase the narrator's name from the tale, you might find yourself thinking that any of the three characters might have uttered the line!
I hope that this helps in your "quest for knowledge" about the letters.