So after all this buildup about one road, which he's looked down for a long time, our speaker takes the other path.
Then we get a tricky little phrase to describe this road. It's "as just as fair." Read without the first "as," this phrase is clear, if you think of fair as meaning attractive, or pretty. But the first "as" makes the phrase a little more difficult. Combining the words "just" and "fair" in the same phrase is a play on words – both of these words have multiple meanings. The phrase could mean something like "as just as it is fair," as in proper, righteous, and equal. But this doesn't quite apply to a road.
Yet we trust that our speaker wouldn't let things get awkward without meaning it. We're guessing that he means the road is just as pretty, but that in the metaphorical world of this poem, he thinks he made the fair, or right, choice.
But it's not fairer – it's just as fair. So he was choosing between two roads, or futures, that were different but potentially equally good.
And having perhaps the better claim, Because it was grassy and wanted wear;
The speaker still seems pretty uncertain when he explains that this second path is better. It is only "perhaps" better.
Then the speaker tells us why the path is better – it seems like it hasn't been walked on very much, because it's grassy and doesn't look worn.
Be careful not to think that the phrase "wanted wear" is personification (it is alliteration, though). "Wanted," in this instance, means something more like "lacked."
Though as for that the passing there Had worn them really about the same,
The speaker of this poem really can't seem to make up his mind! Just when we think we've got a declaration about which path is better, he changes his mind and admits that maybe they were equal after all.
The "as for that" refers to the path being less worn.
"The passing there" refers to traffic, probably on foot just like our speaker, that may have worn the paths down.