The first story of the Shivlingam is mentioned in the Shiv Purana, where the formless Truth manifests Itself as a column of Light whose far ends cannot be known. Brahma ji and Vishnu both are unable to fathom the end of that pillar of Light. Lingam means literally a pillar. Shiva means the auspicious. It is a reference to the Divine Light that is auspicious and governs the Trinity of Brahma, Vishnu, Mahesh. Yoni is the eternal womb of creation. Together, the Shivalingam represents the union of the Ishwara, the passive masculine power, the All-knowing Light and Shakti, the All-powerful feminine. It is the symbol of union of the masculine and feminine elements through which creation begins, the Omniscience and Omnipotence of the Divine, the womb of creation, if you like. The Shivalinga therefore symbolically represents the image of the original union of Ishwara (Sat) and Shakti (Chit tapas) that gives rise to Ananda, the delight that expresses itself in countless ways in creation.
There are of course other meanings given to it, but that is a different matter. Shivalinga becomes a symbolic representation of the Sacchidananda in Its biune poise of Ishwara and Shakti, of the most auspicious and benevolent Light and the ultimate supreme Power of Love. Whatever is poured on the Shivaling flows into the womb of Shakti and from there into the world all around. It symbolises the secret truth that whatever is given to the Divine gets automatically transferred to the whole creation as Prasad. Of course, the offering is an inner offering. The outer acts are symbolic.
Hope this brief explanation helps.
Affectionately,
Alok da


