I'm always amazed how important animals are to us. From Aesop's fables, to gods in the form of cats or snakes, to Brer Rabbit tales - the list goes on and on.
One of the first things children learn is how to make the onomatopoetic sounds that animals make. They learn to sing Old MacDonald and list out animals on the farm. They learn about lions and tigers and bears and elephants. Children in Japan do this also, as do children in France - and I'm sure in many other places also.
As an adult when I was learning foreign languages, I often wondered why it was so terribly important to learn the names of animals. After all, when you're an adult, and you're not likely to meet a lion in the street, why do you need to know what it's called or what sound it makes?
But animals are the basis of metaphors in every language I know.
We know not only what a snake is, and the names of different types of snakes, but also what kind of behavior is associated with snakes and their ilk. We toss off comparisons of people to animals - pigs, dogs, birds, etc. - constantly. Animals also are associated with emotional states like fear, or with personality attributes like slyness.
This is a resource that is often underused in science fiction and fantasy worlds. I have a hard time imagining a population that did not take inspiration in its animals, simply because those animals are resources, by virtue of their interconnectedness in the food chain of any land. I can think of two ways to approach this (off the top of my head).
One, create an animal that is specially relevant to your population for some reason, give it a name, and then start exploring how it could be used expressively in the people's language. In my forthcoming story Cold Words (Analog), for example, the protagonist Rulii compares a human's eyes to those of "the cornered gharralli."
Two, take an existing animal that you are using in your fantasy or science fictional setting, and look for a new twist on its significance. In my Varin world, cats are symbols of selfishness, and I've also designed a species of dog called the tunnel-hound, which is associated with dirtiness.
Take an opportunity to look around for places you can make these connections, and it will help your world take on new dimension.