For some context (and it will probably only make sense if you've read the books I'm afraid) the children and Puddleglum the marshwiggle are looking for the giants' ruined city and words to tell them where to go to rescue Prince Rilian.
They discovered the words "Under Me" in the rocks, and it led them to the underground world where the prince (who is bewitched and clueless of who he really is) is being kept. They get there, and upon finding him, tell him what their quest is, and about how Aslan told them to look for the words, and they found them, right above where they fell down into the underworld. Prince Rilian proceeds to laugh at them and informs them that what they saw is the remains of the engraving on an old tombstone of a giant king, and in full the verse was:
Though under Earth and throneless now I be,
Yet, while I lived, all Earth was under me.
and that it was carved long ago, and not meant as any sign to them.
Upon hearing this, the children are extremely disheartened and figure they probably haven't found the right place after all, at which point Puddleglum interjects with the passage that made me stop and say "Wow!":
"Don't you mind him," said Puddleglum. "There are no accidents. Our guide is Aslan; and he was there when the giant King caused the letters to be cut, and he knew already all things that would come of them; including this."
I knew The Lion, the Witch, and the Wardrobe was allegorical, we all know that, but I didn't remember that clear reference to God's sovereignty in this book! Simply amazing.