The lingam represents the holy union of Shiva who is Soul or Being and Yoni is Citta which is the mind. The lingam is represented as an erect phallus coming from the ground with 1/3rd part within the earth. In mortal world, the semen flows downward, but Yogis make it flow upward to ignite the spiritual fire and go towards immortality. This upward movement of semen is described in Tantra as Urdhvaretas.
With Tapas, the Citta is cleansed of all vrittis, illusions and limitations and Being is realized by shedding all the egos. The union of Being with Citta happens with the destruction of illusion of time and in this Now, Sat Cit Ananda is realized and the Citta realizes it’s true nature. This establishment of the Soul and Citta in the Now leads to intelligence and the Being realizes himself as the Creator. With this union, the Soul does not require any external stimulus or any material attachment with the outside world and lives in cosmic orgasm in a state of Ananda. In this state, He realizes “Aham Brahmasmi” and goes inwards to seek himself as he realizes that his world is within. This is also depicted in art as a Yogi whose eyes are shut with an erected phallus.
Thus Shivalinga is the ultimate symbol of self realization and depicts Shiva as formless, not contained, bounded by any material nature. He existed before the start of time and will be there after the end of everything. He Just IS.