Robert Walton is motivated by both his sense of adventure and a desire to find glory for himself when he ventures into landscapes unknown. He believes that he will find something special, win acclaim, and have a lot of fun in the process. For him, this adventure is what makes life worth living.

In his first letter, Walton is already talking about how the cold breezes remind him of the voyage ahead and fill him with delight. He is so excited to reach new lands that even the thought of it has him feeling happy and upbeat. This is a strong motivation for anyone who desires to travel.

Walton also explains that his wealth—which he grew up with—doesn't offer the same allure as glory. He worked hard to prepare for his trip. He took trips to cold areas to prepare his body for the bracing chill of the North Pole. He studies topics like math, medicine, and physical sciences to prepare for what he might find or hardships he might endure. He writes that he worked harder than common sailors during the day and then passed the night in study.

He did all this because he wants to discover things that have not yet been discovered. He wants the glory of being an explorer. For this, he's willing to leave his home and chart a new course.

In Frankenstein, Mary Shelley offers the character of Robert Walton as parallel to Victor Frankenstein. Both men have embarked on quests, but their voyages of exploration apparently take very different forms. Walton is established as an explorer who literally goes to the ends of the earth. Victor, in contrast, goes as far as he can into the depths of human existence, although he later embarks on a physical voyage as well. The two men are similar in their desire not only to make important discoveries but also to achieve greatness and fame. However, Walton has a strong service ethic: he expects to provide an “inestimable benefit [to] ... all mankind.”

Walton wants not just to go as far as a ship can take him, to reach unexplored territory and to encounter unspoiled terrain, an Eden-like natural paradise remote from the corrupting influence of humans, “never before imprinted by the foot of man.” Hubris is also a strong element of his motivation, for he believes he is uniquely capable of success; the great discoveries he envisions “can only be effected by an undertaking such as mine."

As Walton faces the fact that his own personality is inescapable, he becomes more of a Romantic hero seeking inner truth. While this awareness pushes him to the brink of despair, he fortunately retains enough common sense to reverse his course.

Captain Walton is eager to visit such a hostile environment because he is desirous of making some great discovery that will benefit the human race and win him fame and glory. He says in his first letter,

What may not be expected in a country of eternal light? I may there discover the wondrous power which attracts the needle; and may regulate a thousand celestial observations, that require only this voyage to render their seeming eccentricities consistent for ever. 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.

Walton believes that he will be the first to set foot in this place -- probably because it is so hostile -- and says that he has high hopes for the things he might discover there. It could be this voyage, he says, that explains so many current mysteries. Further, he takes a great deal of pride in being courageous enough to attempt this journey, as he reiterates the fact that no one has attempted it before him. Finally, he longs to satisfy his curiosity.

Moreover, still in the first letter, he writes that

you cannot contest the inestimable benefit which I shall confer on all mankind to the last generation, by discovering a passage near the pole to those countries, to reach which at present so many months are requisite; or by ascertaining the secret of the magnet, which, if at all possible, can only be effected by an undertaking such as mine.

Here, again, we see how much Walton yearns to benefit humanity by discovering a northwest passage that would improve life dramatically by making travel and trade with one part of the world so much more accessible.  Likewise, he believes that only a journey such as this one can help to explain certain secrets of the world.  

His eagerness to visit such an inhospitable place springs from both his earnest desire to know and learn and understand more as well as his desire to be credited with these discoveries forevermore.