Theory:

Then took the other, 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.
Explanation:
 
The poet looked at the other path and decided to go in that way. He says the path he chooses had grass on it which means that it was rarely used. Many people had not walked on this path earlier; that is why this path was of grass. After he walked on the path for some distance, he felt that the path had been worn out the same way the before one and were similar. Even in our life, we take one path or choice, but all of them have the advantages and disadvantages to face.
 
Meanings of difficult words:
 
Numbers
Word
Meanings
1.
FairAs good as the other one.
2.
ClaimBetter option.
3.
GrassyUnused.
Reference:
National Council of Educational Research and Training (2006). Beehive. The Road Not Taken - Robert Frost (pp. 15). Published at the Publication Division by the Secretary, National Council of Educational Research and Training, Sri Aurobindo Marg, New Delhi.