Shiva Linga is symbolic expression of all the deities and represents NirguNa Brahman (formelss Brahman)

At the time, when this incident of mystical Shiva linga had occurred and after which Lord Brahma and Lord Vishnu had stopped quarrelling and started glorifying Lord Shiva, Lord Shiva appeared before them and said,

"I am very pleased with both of you, Both of " O Vishnu! You are the creator, Lord Shiva. This made Lord Shiva extremely pleased and he the preserver as well as the destroyer of this world. I am the supreme you, though having distinct identities have actually manifested from my body-Brahma from my left side and Vishnu from my right." almighty and distinct from all three of you-Brahma, Vishnu and Mahesh. Lord Vishnu expressed his undiluted devotion towards Lord Shiva.

This made Lord Shiva extremely pleased and he said."O Vishnu! You are the creator, the preserver as well as the destroyer of this world. I am the supreme almighty and distinct from all three of you-Brahma, Vishnu and Mahesh."

Linga is the personification of the Almighty God. The term Linga means fusion and the Shivalinga are said to be the symbolical expression of all the deities. 

(Linga Purana 17.2.1)

Origin of Shiva Linga in Linga Purana

 There is a little story of manifestation of Shiva Linga in Linga Purana connecting it with OM

The sages asked Sutji, Lord Shiva is formless then how come Shiva Linga is worshipped? What is the significance of Shiva Linga? What is the proper method of worshipping a Shiva Linga ?

Sutji replied, Once, Lord Brahma and Lord Vishnu developed serious different on the matter of superiority. A tremendous duel broke out between them. As they were fighting a mammoth Linga appeared on the scene, the effulgence of which made efforts both of them amazed. Both of them decided to find out the origin of that divine Linga. Lord Brahma transformed his appearance into that of a swan and flew up in the sky to determine the height of that Linga. Lord Vishnu transformed himself into a roar and entered the depth of earth to find the source of that Shiva Linga. But both of them failed in their objectives and returned to the same place exhausted.

Suddenly, they heard a loud sound of AUM emanating from the Shiva Linga. Very soon, the whole form of OM, consisting of all the three letters A, U and M became visible. (The letters A, U and M symbolize Lord Brahma, Vishnu and Mahesh respectively).

At last, both of them realized their mistake and stopped quarrelling. This way, Lord Shiva was successful in subduing their arrogance. Lord Rudra is beyond sensual perception. He is the supreme Almighty and the bestowers of divine bliss. The mystical form of Shivalinga is a symbolical expression of sacred mantra-AUM. (Linga Purana 17.1.14)

Trinity themselves play different roles in order to teach us the non-difference between them. One becomes a devotee and one becomes deity of worship.