People often misinterpret the poem as being about regretting not having taken the other path, or as being about being brave enough to have taken the "road less traveled by." But Frost himself often commented that people didn't really understand the poem. Let us take a look at the poem, and analyze it stanza by stanza:
TWO roads diverged in a yellow wood,
And sorry I could not travel both
And be one traveler, long I stood
And looked down one as far as I could
To where it bent in the undergrowth;
Here the narator is faced with a decision and, to try to make that decision, he looks as far into the future as possible, trying to calculate the consequences of that decision. But it is in the next stanza where Frost presents us with his insight into the after-the-fact justification of our decisions research into human decision-making (and morals, for that matter) tell us to be what really happens when we make a decision (including a moral action, with justification afterwards).
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,
Here the narrator has clearly made a snap decision to take the other path. We see an immediate justification of the decision: "Because it was grassy and wanted wear," implying that the decision was based on his wanting to take the path fewer people had taken. However, note that in the last line he withdraws that claim by stating that, in all honesty, both paths were worn "really about the same." The narrator doesn't want to admit to himself that his choice was apparently quite arbitrary. Thus, he tells himself a story: that he was chosing a path fewer people had taken. But that is just a story. The truth is that both paths were identical in wear, meaning the same number of people had passed down both paths. The justification for the decision was thus made after the fact, after the narrator had already decided which path to take. We don't like to think there is no reason why we took any given action, so we rationalize -- we create a reason why we took it, placing that reasoning before the decision rather than after, when the reasoning actually took place. The narrator thus tells himself a story of his decision, created after the fact.
We see in the next stanza a continuation of the observation that both paths were (un)trodden equally:
And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!
Yet knowing how way leads on to way,
I doubted if I should ever come back.
He even tells himself that he will come back to walk the other one, and then is honest with himself yet again, saying that he doubted he ever would. This then leads us to the final stanza, where he imagines himself in the future:
I shall be telling this with a sigh
Somewhere ages and ages hence:
Two roads diverged in a wood, and I—
I took the one less traveled by,
And that has made all the difference.
Here he admits that in the future he will stick to his story he told himself about why he made the decision he made: that it was becasue it was the road less traveled by. Indeed, he will in the future only remember the decision this way: that it was a conscious decision to take a road less traveled by, rather than a gut decision he rationalized after the fact. That is the story of his life he tells himself, and it is the one that he tells because it is the most satisfying (thus the sigh of satisfaction). This observation is quite Nietzschean (Nietzsche observed that we are the stories we tell ourselves about ourselves and, thus, we can edit them as well). More, it is in agreement with what neuopsychologists agree to be how we actually make decisions -- and what we do after we make those decisions. They also have shown that when we make a snap decision, we are typically more satisfied with that decision than we are with one where we have done a lot of research beforehand. Even if we do research afterwards on the choices we had. Thus, the narrator of the poem is satisfied with his decision -- precisely because it was a snap decision that was rationalized afterwards rather than a reasoned-out decision. What is most amazing is that Frost understood our decision-making processes better than any psychologist for 80 years after the poem was written.