What is the meaning of the Shiva Lingam?

Answer 1

We shall find, therefore, in this Bhagavad-gita that the complete whole is comprised of the supreme controller, the controlled living entities, the cosmic manifestation, eternal time and karma, or activities, and all of these are explained in this text. All of these taken completely form the complete whole, and the complete whole is called the Supreme Absolute Truth. The complete whole and the complete Absolute Truth are the complete Personality of Godhead, Sri Krishna. All manifestations are due to His different energies. He is the complete whole. . .

The complete whole is not formless. If He is formless, or if He is less than any other thing, then He cannot be the complete whole. The complete whole must have everything within our experience and beyond our experience, otherwise it cannot be complete.
Introduction to Bhagavad-gita-As-It-Is by Srila Prabhupada.

Among the five topics the material cosmic manifestation is created and annihilated again and again. When we speak of creation, Bible says, God said let there be light and there was light. While it is true that God said and there was creation, there is no explanation as to how the creation came in to being. The Lord need not even say anything, just by his will everything happen.

Quoting from authoritative scriptures will answer the question.

Bramha Samhita says,
Krishna who is known as Govinda is the Supreme Godhead. He has an eternal blissful spiritual body. He is the origin of all. He has no other origin and He is the prime cause of all causes.

Verses 7 & 8 of Brahma Samhita explain that Lord Krishna being completely spiritual does not touch the material nature, but glances towards Maya, which is carried by the cit potency. At creation, Shambu a divine halo of the nature of His own subjective portion [svamsa] appears, which is masculine symbol. Ramadevi, the spiritual [cit] potency, beloved consort of the Supreme Lord becomes the corresponding conceiving potencey, which is the symbol of mundane feminine productivity.
verse 9
All offspring of the consort of the great lord [Mahesvara] of this mundane world are of the nature of the embodiment of the mundane masculine and feminine generative organs.
verse 10
The person embodying the material causal principle, viz., the great lord of this mundane world [Mahesvara] Shambhu, in the form of the male generating organ, is joined to his female consort the limited energy [Maya] as the efficient causal principle. The Lord of the world Maha-Vishnu is manifest in him by His subjective portion in the form of His glance.

Srila Prabhupada explains in the The Sri Chaitanya Charitamrita,
The word svanga-vishesabhasa-rupe, indicating the form by which the Lord begets living entities in the material world, is explained herein. He is Lord Shiva. In the Brahma-samhita it is stated that Lord Shiva, who is another form of Maha-Vishnu, is like yogurt. Yogurt is nothing but milk, yet it is not milk. Similarly, Lord Shiva is considered the father of this universe, and material nature is considered the mother. The father and mother are known as Lord Shiva and goddess Durga. Together, Lord Shiva’s genitals and the vagina of goddess Durga are worshiped as the Shiva-linga. This is the origin of the material creation. Thus Lord Shiva’s position is between that of the living entity and that of the Supreme Lord. In other words, Lord Shiva is neither the Supreme Personality of Godhead nor a living entity. He is the form through which the Supreme Lord works to beget living entities within this material world. As yogurt is prepared when milk is mixed with a culture, the form of Lord Shiva expands when the Supreme Personality of Godhead is in touch with material nature. The impregnation of material nature by the father, Lord Shiva, is wonderful because at one time innumerable living entities are conceived.

Answer 2

Lingam means sign. It is a sign of Shiva's power.

Answer 3

Meaning of Shiv ling based on Vedic sources and commentary of Vedic sages such as Swami Vivekanand, Swami Sivanand and Shri Ram Sharma Acharya of Gayatri Parivar(Haridwar).

'Linga' in Sankrit means form or mark and it is shaped like an egg and represents the ‘Brahmanda’ or the cosmic egg. Thus it represents elliptical form of divinity.

A glance at the image of Shiva Lingam shows there is a pillar with three marks and a disc beneath it called 'Peetham' and with a coiling cobra snake around the Pillar and shows its fangs above the pillar.

Shiva Lingam represents the totality of the Cosmos and the Cosmos, in turn, being represented as a Cosmic Egg. Again an egg is an ellipsoid depicting with no beginning, nor end.

Shiva being worshipped as Linga means the Consciousness in its primodal form where consciousness is entering into the Eternal Energy (Shakti).

Base of the ligna is called 'Peetham' and Coiled Cobra snake represents the 'Kundalini' shakti or feminine principle of the divinity whom we refer as Mother goddess. Three rows on pillar represents 'Brahma', Vishnu and Mahesh - different aspects of the divinity.
When un-manifest energy begins to manifest itself, the first form is always the Linga. The word Linga means the form. Why we are referring to it as the form is: the first form in the existence is always a Linga. Linga means a perfect ellipsoid.
The first form of creation is an ellipsoid and final form before dissolution is also an ellipsoid.Thus the first form is a Linga and the final form before dissolution is also a Linga. If you become meditative, your energies will naturally take the form of a Linga.

Thus Linga means Linga means the place of dissolution for the world and all beings. It signifies also Satya, Jnana and Ananta—Truth, knowledge and Infinity. It indicates that Lord Siva is endowed with all-pervading and self-luminous nature. Linga is a symbol which makes us understand the various kinds of Artha which are indicated above.
There are six Lingas, viz., Anda Linga, Pinda Linga, Sadasiva Linga, Atma Linga, Jnana Linga and Siva Linga. These Lingas are taken to mean the characteristics by which the Anda (the Universe), Pinda (the body), Sadasiva, etc., are to be recognized and understood.

Linga is only the outward symbol of the formless being, Lord Siva, who is the indivisible, all-pervading, eternal, auspicious, ever-pure, immortal essence of this vast universe, who is the undying Soul seated in the chambers of your heart, who is your In-dweller, innermost Self or Atman, and who is identical with the Supreme Brahman.

Answer 4

This might sound weird, but it is a penis. There's nothing nasty about it--it's about God's generative power. It came from a time before people thought of sex as something to be ashamed of.

Answer 5

Shiva's pee pee.