The story of the appearance of the Shivling is mentioned in numerous Puranas. The Shivling Story begins with Brahma and Vishnu getting into an argument. Vishnu and Brahma wanted to know who was superior and this led to a fight. Shiva intervened and said whoever can find out the origin or end of Shivling is superior. Shiva appeared before them in the form of a huge pillar of fire. Vishnu went down searching and Brahma went up searching. Both traveled and traveled but never reached the beginning or end.
After the futile search, Vishnu and Brahma prayed to Shiva and appeared before them in the form of Jyotirlinga and this day of the appearance of Lord Shiva is celebrated as Shivratri. This Linga form of Shiva is also known as Lingodabhavamurti.
Shivling is a symbol. Shivling is the energy that sustains the universe. All animate and inanimate are born and transform (die) in this energy. Only this energy exists. Rest all are forms in this energy like bubbles on water.