Epigraphs are like little appetizers to the great main dish of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
Sleep is not, death is not;
Who seem to die live,
House you were born in,
Friends of your spring-time,
Old man and young maid,
Day's toil and it's guerdon,
They are all vanishing,
Fleeing to fables,
Cannot be moored.
What's up with the epigraph?
This is a passage from Emerson's Conduct of Life, and once you read Miss Peregrine's Home for Peculiar Children, it feels like Riggs crafted the book with this snippet in mind. Let's go line by line here, shall we?
Sleep is not, death is not; who seem to die live.
This could refer to the fact that Grandpa's friends from the 1940s, who should all be dead by this point, are still alive. Also, Enoch has the power to bring dead people back to life temporarily, like the piemaker from Pushing Daisies.
House you were born in, Friends of your spring-time, old man and young maid.
Jacob must return not to the house he was born in, but to the house his grandpa, an old man, was born in. Jacob looks like his grandpa looked at that age, so it's almost like Grandpa is returning home in spirit. Grandpa's ex-girlfriend, Emma, is still there, but since she's in a time loop, she's not in her eighties—she's still a young maid.
Day's toil and it's guerdon, they are all vanishing.
What's a guerdon? A guerdon is a reward. In this book, we have day-to-day life's rewards not being that interesting anymore—Jacob is tired of his ordinary life, so he decides to stay in the world of the peculiars at the end of the book.
Fleeing to fables, cannot be moored.
Jacob thinks Grandpa's stories are tall tales, but in the end, he realizes they're real, and he leaves his world to stay in the peculiar world—"fleeing to fables." And as for "cannot be moored," well, they literally get in boats at the end of the book and sail away, unmoored. Plus, as the book ends, the loop's come undone, unmooring the lives of the peculiar children.