As already mentioned here by Dr. R N Srivastava, In Hindu Mythology, Brahma, Vishnu, Mahesh (Shiva) are the trinity, the creator, the protecor and the destroyer. "Ling" means symbol. So, shivling actually is symbolic representation of Lord Shiva. This also represents a devine symbol of supreme being present in all living creatures.
If the word ling is bifurcated and studied in sanskrit, it being composed of laya and agaman refers to dissolution and recreation respectively. Thus , it symbolizes both the creative and destructive power of Lord Shiva and thus a great sanctity is attached to it by the devotees.