The less well-traveled road is a metaphor for the kinds of choices we make in our lives. Choosing the less-traveled road means following a path that is not followed by the majority of people in our situation. All through our lives, we are confronted with choices, and because we cannot lead parallel existences, really, no matter which road we choose makes a difference. But to choose the less popular choice says something about one's spirit of adventure, the willingness to take a chance, the ability to think for oneself and not be a follower, an openness to a different kind of life than people expect of us or that we expect of ourselves.
Choosing the less-traveled road might be choosing a mate that is from a different culture or country. It might be pursuing a dream as an artist, rather than going to college, as most young people are expected to do. It might be running off and joining a carnival or giving up one's job to write a novel. These are all instances of the less well-traveled road, and I have chosen these to highlight how different a person's life will be, having made one of those choices. If we choose the more well-traveled road, we know what to expect. Others have been there before us. There are fewer surprises, less chance for serendipity. That's a very big difference.
I think that in today's world, the distinction the narrator makes in the poem is more opaque, since our choices feel far more complex than a choice between roads more traveled and less traveled. But the fact remains that no matter how complex our choices are, eventually, they do get narrowed down to two choices. Go right or go left. Marry this person or that person. Attend this college or that college. One of these is bound to be less traveled than the other. And of course, this has to make a great difference in one's life. These are formative and transformative choices, and after we have made them, we are not the same people we were.