The poem appears to be the thoughts of the poet Frost himself, and he has confirmed this in public appearances. It is the poet reflecting on a career choice he had made way back many years earlier. The whole poem is a long metaphor. The "roads" symbolize the choice he had to make at a critical point in his life between pursuing a conventional but secure career, perhaps as a college professor, and the alternative of leading an insecure and simple life while pursuing his true interest as a creative writer. We have to assume that by the road "less traveled by" he means he chose the road that fewer aspiring creative writers have chosen because it was, after all, too much of a gamble. As to why Frost took the "road" he did, it was evidently because of his belief in his talent and because of his admirable strength of character.
Then took the other, as just as fair,
And having perhaps the better claim,
Because it was grassy and wanted wear;
Though as for that the passing there
Had worn them really about the same.
Frost's poetry is full of descriptions of the kind of austere life he was leading. "Mending Wall" is a good example, as is his "Stopping by Woods on a Snowy Evening," "Two Tramps in Mud Time," "Death of the Hired Man," and many other poems about the life of a simple New England farmer.
When Frost was asked on one occasion what he had meant by saying: “I shall be telling this with a sigh,” he told the questioner (I believe it was a college girl who asked him that specific question in a letter) that he was really only kidding. He did not regret the choice he had made to live a simple life and devote himself to his poetry. Frost had become a great success and was considered the best American poet of his time.
Many young people who aspire to careers in one of the arts--creative writing, music, painting, acting, or whatever--have to make a similar decision. It is extremely hard to make a living in the arts because there is so much competition and so much insecurity. Most end up taking the other "road," which often involves a compromise such as becoming teachers, commercial writers, copywriters, commercial artists, or some other alternative.
To write prose and verse, to hammer out little tunes on the piano, and to draw and paint, are instinctive with a great many young persons. It is a form of play, due merely to the exuberance of their years, and is no more significant than a child’s building of a castle on the sands....The point I want to make is that this facility is, if not universal, so common that one can draw no conclusions from it. Youth is the inspiration. One of the tragedies of the arts is the spectacle of the vast number of persons who have been misled by this passing fertility to devote their lives to the effort of creation. Their invention deserts them as they grow older, and they are faced with the long years before them in which, unfitted by now for a more humdrum calling, they harass their wearied brain to beat out material it is incapable of giving them. They are lucky when, with what bitterness we know, they can make a living in ways, like journalism or teaching, that are allied to the arts.
Somerset Maugham, The Summing Up