El-ahrairah pretty much always wants to (a) eat and (b) protect his people. There's not a lot of room for character growth in that, but there is a lot of room to think about the El-ahrairah myths as a symbol—say a couple of paragraphs' worth of room.
First, El-ahrairah is pretty close to being a perfect Chief Rabbit, as we noted on his character page. The only problem he has is that occasionally his trickster nature gets the better of him, as when he choses to make a joke about Frith rather than listening to him, which results in Frith making a bunch of predators. So El-ahrairah serves as a symbol of what Hazel and the other Chief Rabbits should be; and an ideal to compare them to.
In fact, the first time we hear about El-ahrairah, it's because Dandelion is comparing Hazel to that hero and Hazel recognizes this as a compliment: "It was warm praise and cheered him" (5.10). That's a pretty simple sentence, but it nicely mixes in Hazel's feelings—the praise is warm, it cheered him. (And to be clear, words can't really be warm, so when we hear that this praise is warm, we know that we're hearing about the feeling those words cause.) Whenever Hazel comes up with a clever plan, he gets compared to El-ahrairah, as with his plan to use Kehaar to scout out the land (23.117). To be compared to El-ahrairah is a very good thing since he's the ideal model of a Chief Rabbit.
Second, El-ahrairah's name reminds us that the world is a very dangerous place for rabbits. We say "El-ahrairah" (actually, we're saying it a lot these days), but his name is actually Elil-Hrair-Rah.
All together his name means "Enemies-Thousand-Prince" or "Prince with a Thousand Enemies." So, in this dangerous world, where the rabbits face a thousand predators, they need a rabbit as clever as El-ahrairah to protect them.
Third, El-ahrairah and the tales about him serve as a reminder of community for the rabbits. That is, the stories about El-ahrairah are the sort of oral folktales that every rabbit knows. We know this because the narrator directly tells us during the first El-ahrairah story we hear: "All the rabbits had heard the story before: on winter nights, when the cold draft moved down the warren passages and the icy wet lay in the pits of the runs below their burrows; and on summer evenings, in the grass under the red may and the sweet, carrion-scented elder bloom" (6.7).
All the rabbits know this story and it's a constant factor in their lives, from winter (when you tell stories indoors) to summer (when you tell stories outdoors). The narrator spends a lot of time there describing the changing weather from winter to summer, which emphasizes what doesn't change: the storytelling.
That's why it's so shocking when the rabbits in Cowslip's warren don't seem to know or care for the story Dandelion tells. When Cowslip says that this story is "An unusual tale," Blackberry responds with surprise: "But he must know it, surely?" (16.5-6). That "surely" at the end captures that surprise that Blackberry and Hazel's rabbits must feel about Cowslip's rabbit not responding to this story.
This lack of interest in El-ahrairah stories is one of the strongest reminders that the rabbits in Cowslip's warren aren't like regular rabbits anymore. When they don't seem to know or like these traditional stories, what they're really saying is "We don't really belong to the same community."
Fourth, though rabbits die, their memory can live on in El-ahrairah myths. We see this at the end in two ways, one obvious, one less obvious. Obviously, we hear about Woundwort becoming a mythological figure: "And yet there endured the legend that somewhere out over the down there lived a great and solitary rabbit, a giant who drove the elil like mice…" (Epilogue.3). We also hear that Woundwort is remembered as the Black Rabbit's cousin. This legendary version of Woundwort emphasizes his power and danger, which is how the rabbits of Watership Down remember him.
The less obvious example of a living rabbit becoming a myth is when Hazel's own adventures get turned into more El-ahrairah stories. In chapter 50, Vilthuril tells her cubs a story about swimming a river (chapter 8), going through a lonely place (chapter 10), and going through Cowslip's warren (chapters 12-17). It took us a few readings to notice that Vilthuril is telling Hazel's story as El-ahrairah's story (50.43-46). (We didn't notice it at first, but Hazel gives a big hint when he notes that this story seems familiar.) So Hazel's stories will live on as El-ahrairah stories—which will keep alive Hazel's virtues and ideals for other rabbits to be inspired by.