This seems to be a case where we have to assume that the speaker is Robert Frost himself and that he is referring to the choice he made in how to live his life. We know what that choice was from the way he actually lived. He lived a very quiet, uneventful life in New England, doing a lot of his own farm labor and maintenance work. He chose peace, quiet, simplicity, and harmony with nature, not unlike Thoreau and Wordsworth before him. The alternative, the other road, would have been to pursue material success, which almost certainly would have meant moving to a big city like New York and possibly getting a job as a teacher, meeting important people, socializing, publicizing himself, living a hectic, competitive, urban life, as so many writers have done. These are two "roads" that go off in different directions, and no one can follow both. Frost was noted for his modesty and simplicity, which shows in almost all his poetry. He was well loved by the American people because of his personality as well as his writing.