There isn't a single epigraph to the whole book, so we can't easily say "Well, the epigraph expresses themes X and Y which we see in the book." But every single chapter contains some epigraph, each of which does two things for us.
(1) The epigraph is often from some pretty difficult book or poem. For example, the first chapter contains a quote from the classic Greek tragedy, Agamemnon, which you might not expect in a book about adventurous bunnies; and some of the epigraphs aren't even in English, like chapter 7's French quote from Napoleon about courage. These are serious epigraphs, dude.
But that seriousness might be part of the point. By putting in these serious epigraphs at the beginning of serious chapters, Richard Adams reminds us that these serious rabbits are engaged in serious business. There is tragedy here, as much as there is in the Greek Agamemnon, thank you very much. And these rabbits are as brave (in their way) as Napoleon. So, yes, we're reading a fun book about bunny adventures; but we're also reading a book about death, about finding your place in the world, about sacrifice.
Bunny sacrifice, sure, but still sacrifice.
(2) Every epigraph gives some hint about what's going to happen in the chapter. It may not always be obvious, and sometimes you might have to reread to understand the hint.
For example, take the epigraph to chapter 3, "Hazel's Decision":
What am I lying here for?... We are lying here as though we had a chance of enjoying a quiet time.... Am I waiting until I become a little older? - Xenophon, The Anabasis (3)
If you know who Xenophon was, you're probably a scholar of Ancient Greek. If you don't, we'll tell you that Xenophon was a soldier who led his Greek mercenaries out from behind enemy lines.
But, hey, even if we don't know any of that handy cocktail party fodder, the epigraph still foreshadows what's to come. Here's some guy asking why he's "enjoying a quiet time" when they really don't have the time for some R&R. What is he waiting for? If the only reason to wait is to get older, well, that's a terrible reason to wait. Now is the time for Xenophon to act.
And then, when we read the chapter, we see that Hazel has to make a decision: should they leave the warren and when? (Okay, you don't have to read the whole chapter to get that—the title kind of hints at that since it's "Hazel's Decision.") But when we put the epigraph and the chapter together we see that Hazel is like Xenophon, if you substitute "rabbit" for "Ancient Greek": he's the leader of a group of Ancient Greeks/rabbits who has to act now. (And if you know who Xenophon is, then you know that Hazel, like X, has to act now in order to bring his followers to safety.)
Or take the epigraph to chapter 35, "Groping": "This world, where much is to be done, and little known... - Dr. Johnson." It's a little strangely put, but the idea here is pretty simple: we live in a world that's is full of stuff that we don't know about. And this is exactly the situation that Bigwig is in when he enters the "world" of Efrafa. He has to break out the does, but he's only now learning about how totally controlled this warren is. Again, the epigraph here really works with the title of the chapter. Bigwig is groping for answers to all the unknowns in this world.
In that way, this epigraph hints at what Bigwig is going to face (uncertainty) in the same way that chapter 3's epigraph hints at what Hazel is going to have to face (a decision to act). We could go through all the epigraphs, but—according to Richard Adams's daughter Juliet in the book's introduction—part of the fun of the epigraphs is that "when you read one for the first time, you can't imagine how it is going to have anything to do with the story; and then, as you read on, you see how it does."