The Unicorn symbolizes purity, honestly, hope, and divine connection.
The Unicorn is likened to Man - part animal, part divine. His fierceness and savagery represent and signify the animal nature. His whiteness represents purity, and signifies the divine nature.
The taming of the Unicorn by the touch of the virgin signifies the taming of the animal nature in man by the awakening influence of his higher self, or soul, symbolized by the virgin. The long horn symbolizes the achievement of right fusion or the integration of man's lower and higher self. “
In terms of the symbolic nature of the unicorn, whether it existed or not doesn’t really matter. Mythological creatures are a reflection of man's hopes and fears, dreams and nightmares, and inner consciousness. Such creatures tend to represent man's worst traits, but the unicorn is an exception to this general rule. 
