One of the difficulties that Ponyboy and the other greasers face is the idea that they are stuck where they are, that they don't have the options that the Socs do. Darry is stuck because he has to take care of the other boys, Dally is so dragged down by his rough childhood and criminal record that he can't change his lot in life, Ponyboy expects that he too will end up this way.
But, as he is dying, Johnny sees that it doesn't have to be that way. He interprets the poem to suggest that there is a possibility for any boy, even a greaser like Ponyboy. Johnny's understanding, gained only as he lies on his deathbed, allows Ponyboy to start seeing the same realization. He then begins to write his "theme" in the hopes that people will understand greasers like Dally and respect them instead of looking down on them. This beginning may in fact signal a new beginning for Ponyboy, a way out because if he does a good job he can keep up his grades and save that potential he has.
Johnny's letter from the grave helps Ponyboy move on and opens up that world of possibilities for him.