In Letter One, of Mary Shelley's Frankenstein, Robert Walton openly states his reasoning behind his expedition to the north.
I may there discover the wondrous power which attracts the needle; I shall satiate my ardent curiosity with the sight of a part of the world never before visited, and may tread a land never before imprinted by the foot of man.
Essentially, Robert Walton desires a few things to come out of his expedition. First, he wishes to discover the "seat of magnetism." This means that he desires to find the place on Earth which regulates the magnetism. Second, Walton wants to see a place no other man has ever seen. On top of that, not only does he want to see an unexplored area, he wishes to be the first one to set foot upon an unexplored territory. He wants to be the first one to place a footprint upon a never before touched place. Outside of that, Walton knows that his travels could result in a new path which other travelers and shippers could use.
In the end, Walton is simply seeking personal and historical renown. He wants to be known for doing/finding something which no others have ever found before.
Mary Shelley's Frankenstein includes a series of letters which affect the events in the story. The first of these, written by an explorer named Robert Walton to his sister back in England, Mrs. Saville, is sent from St. Petersburg, Russia and discusses Walton's upcoming voyage to the North Pole. He reveals that he has spent six years preparing for and planning this trip, and that he plans to leave the following June. He will soon make a trip to Russia to find the right ship for the voyage and to finalize plans for the journey.
Walton recalls his father telling his uncle that Walton should not be a sailor. He also recounts his failure to make a career out of writing poetry. These are two motivations for his expedition: to prove his family wrong and to make up for his previous failures. He implies in his letter to his sister that he wants to know and learn more about the world, and that he cannot learn these things sitting at home and writing about them.
In summary, Walton desires to take this trip in order to show his father and uncle, as well as himself, that he can do something of worth and importance to the world. He can discover new things and learn new information to share with others. His self-image and his persona to others will undertake a transformation, should he return alive and successful.