The jyotirlinga is the supreme partless reality, out of which Shiva partly appears. The jyotirlinga shrines, thus are places where Shiva appeared as a fiery column of light.
As per the Shiva Purana, Brahma and Vishnu once had an argument over who was supreme in the creation. To test them, Shiva pierced the three worlds as an endless pillar of light, the jyotirlinga. Vishnu and Brahma decide to travel along the pillar downwards and upwards respectively, to find the end of the light. Brahma lied that he had found the end, while Vishnu conceded his defeat. Shiva appeared as a second pillar of light and cursed Brahma that he would have no place in ceremonies while Vishnu would be worshipped till the end of eternity.