modelled these verses on a passage in the "Wanderer," an elegiac lament telling the story of an exile who has been banished and, wandering weary in foreign lands, seeks to return to his home. 
     It is perhaps peculiarly apt that Aragorn ("Strider"/"Wanderer") recites these lines.  But, the lines are to refer to Eorl the Young who came to settle in Calenardhon; and from Unfinished Tales we know that the Éothéod had been driven from their homeland and had been wandering from land to land for some time before Cirion gave to them Calenardhon.  So, the verses have an ironic (though in a good sense) appropriateness for the wandering Éothéod as well.  
     There's rather more to say about Tolkien's use of these lines, but I don't have the time right now (I'm on my lunch break at work).

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All that is gold does not glitter,
Not all those who wander are lost;
The old that is strong does not wither,
Deep roots are not reached by the frost.
From the ashes a fire shall be woken,
A light from the shadows shall spring;
Renewed shall be blade that was broken,
The crownless again shall be king.