Across cultures and times, the unicorn has been seen as a universally positive symbol, representing chaste love, health, harmony, and the untamable. In western culture, the unicorn has been a powerful symbol for many years, carrying many positive implications that are still part of its myths today. Many eastern cultures have similar creatures like the kirin and the karkadann, often with strikingly similar associated concepts.
The connection between the unicorn and purity is commonly known, with many images existing of a pure virgin taming a unicorn with her presence. This concept seems to have originated with an analogy representing the incarnation of Jesus that showed the Virgin Mary taming a unicorn. The symbolism was clear - a pure, virginal figure being the only one who was able to contain and "tame" a holy, mystical force. The connection between the unicorn and purity became more defined in the 13th century, where it became seen as a symbol of devotion to a pure lady. Soon the idea of the unicorn as a symbol of pure, chaste love became popular. The unicorn also has connections to other forms of purity as well - its horn, made of a material known as alicorn, was thought to be able to combat poison and disease. Interestingly, many cultures have creatures much like the unicorn (such as the camahueto of Chiloe myth and the karkadann of Near Eastern myth) that also have horns that are thought to cure diseases or neutralize poison.
The unicorn is also strongly connected to the idea of freedom. While they could be tamed by pure maidens, it was impossible for anyone else to capture one, and they defied all attempts. The Bible contains unicorn-like creatures that are associated with freedom from slavery and amazing strength. Heraldry also uses the unicorn in a similar fashion, with unicorns breaking out of chains being used as a symbol of liberty for the user of the crest and unicorns bound in golden chains and crowns serving as a boast of sorts, the idea being that the bearer of the crest is able to tame the untamable. While unicorns may be seen mostly as gentle, the fact remains that they are also a symbol of strength and freedom at all costs.
Creatures similar to the unicorn exist in other cultures as well, and many of them have similar associations. One of the better known is the kirin (the Japanese variant of the Chinese Qilin, which looks much less like a unicorn), which is thought to be a symbol of benevolence and harmony. Kirin were thought to only appear in lands with a benevolent ruler, and while they were gentle in most cases, they would defend anyone pure violently against harm. They were also thought to be the pets of the gods. Because of this, the kirin primarily symbolizes of peace, protection, and divinity - quite similar to the pure, holy unicorn.
The unicorn is a very positive and affirming symbol, showcasing the best of love, strength, and purity. Unicorns have always been associated with good in nearly all cultures. Perhaps there is power to this symbol.