In The Outsiders, what does the poem mean and how is it relevant to the book?
You might want to consider how one of the characters interprets the poem himself. At the end of the book, in the last letter that he writes to Ponyboy, Johnny declares that he understands the poem now. Note what he writes:
I've been thinking about it, and that poem, that guy that wrote it, he meant you're gold when you're a kid, like green. When you're a kid, everything's new, dawn. It's just when you get used to everything that it's day. Like the way you dig sunsets, Pony. That's gold.
Consider the importance of sunsets in the novel and how it seems to be a vital link to humanity. Ponyboy, for example, feels kinship with Cherry, even though she is a Soc, because she likes looking at sunsets.
The poem as a whole, though, seems to use the beauty of Spring's first blooming as a metaphor for growing up. The "first leaf" of nature is described as "gold," which is "the hardest hue to hold." The reference to "Eden sank to grief" seems to imply that this initial innocence and beauty is lost with time and ageing, just as Adam and Eve lost their place in the Garden of Eden. The poem concludes with the inevitable process of ageing and how nothing can stay in its "golden" state:
So dawn goes down to day,
Nothing gold can stay.
Johnny's last words to Ponyboy are to try and stop this inevitable process by not losing sight of the important things in life: sunsets and the beauty of nature. Unfortunately, other characters have lost sight of this, have lost their "golden" qualities because of their social situation. Johnny urges Ponyboy not to do so and to retain something of that "golden" innocence of nature in first Spring.