I agree with Caitlin and Tyler both. I think the 'claim' means the nicer looking one. Just like you would look at a piece of land in the old pioneer days and choose the nicest part for your 'claim'(declare the land as your own). You should look up the word claim and see the many definitions to fully understand the idea of it.

It means that the path would actually be the better choice, because less people have gone down it.

In my understanding, a claim is usually equivalent to a demand or to exercising your right to choose. In this case I think "he" was drawn to this path, not exactly knowing why. Would it be fair to say that Frost suggests "the road claimed him"? ....Now, afterwards he is reflecting on the impact of that choice. What then seemed to be an intuitive decision, turned out to have made all the difference. What I like the most about this poem is that it reminds me to let my intuition guide me and I will be all right.

Here, Frost is saying that he took this road because it was better to him, for whatever reason. So "claim" means something like "merit." It has better claim, in that it was more interesting, or moving to him.