In Frankenstein, Victor tells Robert Walton his story because he sees something of himself in the young man. They are both single-minded, self-taught explorers. Victor explores the depths of science, and Robert quite literally explores the world. They are both also very lonely in their endeavors, something that Victor recognizes. However, Victor is much further along in his journey and has already experienced the pitfalls and tragedies that his pursuits have caused.
Recognizing something of himself in Robert, Victor decides to tell him the story of his monster as a sort of warning. He sees that Robert is willing to go to any length, even putting himself and others in mortal danger, to achieve his goals. Victor has already learned the folly of such single-minded pursuits. He wants to talk some sense into this intrepid and foolhardy arctic explorer. Victor's story is meant to curb Robert's enthusiasm and hubris and convince him that the pain and tragedy of such things are not worth it in the end.
Ultimately, Victor succeeds. After hearing Victor's tale, Robert decides to abandon what would likely be a suicide mission. He turns back for England before reaching the North Pole after realizing that nothing is worth the price that Victor paid for his own adventure.