Symbolism, Imagery, Allegory
Unicorns aren't just a figment of Western European imaginations. Nope—in The Ropemaker they're the most important residents of the Valley's cedar forests (3.199). They are really the ones that the Urlasdaughters have been singing to for many years. By keeping the unicorns happy, the cedar forests are happy, and the magic (present in the trees) stays all good (3.209). The unicorns will stay so long as the magic's fine, but if the magic leaves then the unicorns will freak out and flee the Valley. As Meena says:
"But my ma told me she thought the real magic was in the cedars. That's why we have to go to the lake to sing to them. The unicorns only do what they do, just by being there and being so scared of men. And if the cedars weren't there, or if they lost their magic somehow, then there wouldn't be unicorns anymore." (3.215)
So basically the unicorns symbolize the larger health of the Valley itself. When the cedars are fine and the Valley is protected from the threat of the Empire, the unicorns aren't temperamental. But when this dynamic begins to shift, the unicorns are the first sign—or symptom, to use a health term—that something's awry.
But we don't have to just take Meena's word for it. We can also look at it this way: The first problem in the book is Tilja's mother's disappearance—and she goes missing while chatting to the unicorns and gets bopped on the head by the Ropemaker in the form of a giant unicorn. In other words, unicorns are woven through the very first time thing that goes wrong in The Ropemaker—which lets us know that they're good indicators of problems in this book.
And in case you're thinking that unicorns seem like more trouble than they're worth—after all, folks who know about them have to keep pretty quiet lest other people think they're crazy—rest assured that the unicorns earn their keep. It's only thanks to the unicorns that men get sick if they go into the forest, and it's this sickness that keeps the Emperor's evil army away from the Valley. If the unicorns disappear, it's curtains for the Valley.