The poem from The Outsiders that you refer to is, of course, Robert Frost's "Nothing Gold Can Stay." It is one of Frost's most famous poems, and the book in which it was originally included (New Hampshire) won the 1923 Pulitzer Prize for Poetry. Basically, the poem represents the experiences of life and how the innate goodness and innocence of youth is often hard to hold. The poem includes references to the Garden of Eden, where its innocent inhabitants, Adam and Eve, fell victim to the original sin.
In Johnny's farewell letter to Ponyboy at the end of the final chapter, the dying greaser explains the poem to his friend.
You're gold when you're a kid, like green. When you're a kid, everything's new, dawn. It's just that when you get used to everything that it's day. Like the way you dig sunsets, Pony. That's gold. Keep that way.
The poem is used in part as a reminder to Pony that he is still young and has a long life ahead of him--one which he can still control. Johnny hopes that there is still time for Dally to turn his life around as well, but unbeknownst to Johnny, Dally has already decided that life is no longer worth living.