What influenced the traveler's choice?
The traveller in this poem makes clear the fact that, if at all possible, he would have liked to have been able to traverse both roads: "sorry I could not travel both / and be one traveller."
However, after having studied the two for a long time, he chooses not the first he had studied, but "the other, just as fair." His reasoning, he knows, does not stand up to close scrutiny. It is almost arbitrary, but the path he chooses has "perhaps the better claim / because it was grassy and wanted wear." That is, upon first observation he feels that this path is in need of more use than the other due to its grassiness.
However, upon beginning to walk down it, the traveler notes that "the passing there / had worn them really about the same." The poet then goes on to describe the paths again as having lain "equally" before him. The point of the poem is that the choice of one path over another is often arbitrary, influenced by something minor that, in retrospect, seems meaningless, and yet no one path in life is obviously better or worse than any other.