The speaker of the poem is walking through the woods when he comes to a fork in the road. It splits into two different paths, and he is forced to choose which path he wants to take. It is rather difficult to decide, however, because the paths look different at first but have really been "worn ... about the same" due to the relatively equal number of people that have taken each one. The speaker claims that both paths "equally lay / In leaves no step had trodden black" on that particular morning.
However, in the final stanza, he switches from describing his past experience with the two roads to describing what he means to do in the future. He will tell a story that is not actually true: that when he came to a fork in the road, he took the road that fewer people had traveled, and that this has "made all the difference" in his life. In other words, he will claim to have taken the road "less traveled," and he will tell people that this unique or brave choice has had a significant impact on his life—that it has, perhaps, changed the course of his life irreversibly and in important ways.
The "difference" he refers to in this fiction is the supposed difference between what his life would have been like had he not chosen the "less traveled" road and what it has been as a result of his choosing it.