To obtain the nectar of immortality, the gods and demons churned the ocean, using Mount Mandara as the churning rod and the serpent Vasuki as the rope. Before the nectar, a terrible poison called Halahala came out, and its flames began to burn the whole of creation.
When all the gods came to him for refuge, Shiva, the ocean of compassion, drank the poison. Mother Parvati held his throat so that the poison would not go down. The poison turned his throat blue, and so he came to be called "Neelkanth", the blue-throated one. This story carries the message of bearing pain for the good of others.
In another story, King Bhagiratha performed fierce penance to bring the heavenly Ganga down to earth to free the souls of his ancestors. But the Ganga's force was so mighty that the earth could not bear it.
At Bhagiratha's prayer, Shiva caught the Ganga in his matted hair and then gently released a single stream onto the earth. And so he is called "Gangadhar", the bearer of the Ganga, and the tradition of pouring water over the Shiva linga is linked to this story.