In a heist film, there's always a character who has psychic or mystical powers—and here, that character is Fiver. Wait, what? Heist films never have psychic/mystical characters? Oh, in that case, we don't know what Fiver's doing here. Let's start again.
This little guy's Hazel's smaller brother and he always seem afraid. When we first meet Fiver, the narrator comes out and tells us that he's pretty much always worried. Compared to Hazel, he "seemed less at ease" and he has the habit of turning his head and looking around him "which suggested not so much caution as a kind of ceaseless, nervous tension" (1.5).
We love that sentence (we do) because it very neatly tells us that Fiver is nervous and that this isn't just the useful "caution" that rabbits need. Then, just to drive home the point, Fiver jumps away from a harmless bee and the other rabbits point out that he's a scaredy rabbit. So Fiver is The Frightened One.
But there are a handful of times where Fiver is the only rabbit who isn't frightened. For instance, Fiver isn't frightened of the man-made iron tree (really a pylon) that the rabbits find near Watership Down (18.2). And Fiver is the first rabbit to cross the bridge over the River Test when they are raiding Efrafa for does. In fact, Fiver seems so brave about bridges that Hazel jokes that Fiver "simply loves crossing bridges" (33.57). Hey, everyone needs a hobby.
Maybe we should say that Fiver kind of always has the "wrong" reactions to things—though he always turns out to be right in the end. He's not afraid of the bridge (when the others are), but he's afraid of staying in Cowslip's warren (when the others aren't). Eventually we figure out that Cowslip's warren has lots of dangers and the bridge is totally safe.
Fiver's not afraid of raiding Efrafa, but he is nervous about Hazel going to Nuthanger Farm to free the domesticated rabbits—and Nuthanger Farm winds up being the place in which Hazel nearly dies. Even at the end, when there's war on, he seems to be having the "wrong" reaction: when Vervain comes to kill Fiver, Fiver doesn't attack or run away or curse Vervain. He simply says "I am sorry for you with all my heart. […] Believe me, I am sorry for your death" (47.71-3). That's pretty spooky, but it fits with Fiver's character since he often reacts opposite to how the other rabbits expect him to react—and he's always right.
To sum up, Fiver is mystical, and Fiver is often frightened. Except when he's surprisingly brave or doing the opposite of what most rabbits in his situation would do.
But above all, Fiver is a plot device. That may be hard to hear if you love Fiver, as we do. But Fiver's most important role is that he tells the other rabbits something they need to know but couldn't really know otherwise.
For an experiment, take Fiver out of the book and see what happens. Without Fiver, the rabbits don't know that Sandleford Warren is doomed, so most of them die. But let's say a few escape and they go over to Cowslip's warren, where they can relax and eat nice food… and then get caught in snares since Fiver isn't around to warn them. Even if a few of the rabbits escape that death-trap, they don't know where to go since it's Fiver all along who has been pushing to go to Watership Down.
So Fiver knows things that help to keep the story moving, which means that—like it or not—he's a plot device. Sorry Fiver-fans.
It might seem weird for a rabbit to have psychic or magical powers, but it fits in with the classical Greek and Roman epics that are in the background for Richard Adams. For instance, the great hero Aeneas gets some help from the prophet Sibyl in the Aeneid and Agamemnon gets help (not really) from the prophet Cassandra. So, a bunny having psychic powers might be weird, but it fits with the epic nature of the book.
Sidenote: we love what the publisher Rex Collings wrote to a friend when he accepted Watership Down: "I've just taken on a novel about rabbits, one of them with extra-sensory perception. Do you think I'm mad?" (source) So even Rex recognized that psychic bunnies were a little odd.