The lingam (also linga, ling, Shiva linga, Shiv ling, Sanskrit: लिङ्गं,liṅgaṃ, meaning "mark", "sign", or "inference") is a representation of the Hindu deity Shiva used for worship in temples. In traditional Indian society, the linga is rather seen as a symbol of the energy and potential of God, Shiva himself.
The lingam is often represented alongside the yoni (Sanskrit word, literally "origin" or "source" or "womb), a symbol of the goddess or of Shakti, female creative energy. The union of lingam and yoni represents the "indivisible two-in-oneness of male and female, the passive space and active time from which all life originates".
Linga represents Cosmic Egg ('Brahmanda' in Sanskrit) who has neither beginning nor end. It is believed that this changing world ('Jagat' in Sanskrit) merges or dissolves into the Formless in the end. So, the Linga is the simplest sign of emergence and mergence.
The Sanskrit term लिङ्गं liṅgaṃ, transliterated as linga, means, symbol. There is wrong impression of using it as ‘phallus’ which is known as "Shishan" in sanskrit. Most common use of linga is used as gender symbolization for eg. 'Pulling' means male(Purush) gender(symbol) puṃliṅga and 'Istriling' specify female gender (Istri-symbol)strīliṅga. Shiva Lingum, therefore, symbolizes formless Lord Shiva's and as such considered most sacred by Shaivaites sect of Hindus.
लिंगार्ध गमकं चिह्नं लिंग मित्यभिधीयते। लिंगमर्धं हि पुरुषं शिवं गमयतीत्यतः॥ शिवमहापुराण विद्येश्वरसंहित
"A characteristic sign by which one can recognize something is known as his Linga. Sivalinga is a *sign* which recognizes the Supreme God Siva."
Some scholars argue for different kiddiings and uses, ranging from mark, sign or characteristic etc. Vaman Shivram Apte's Sanskrit dictionary provides these definitions:
The Hindu scripture Shiva Purana also describes in its first section, the Vidyeshwar Samhita, the origin of the lingam, known as Shiva-linga, as the beginning-less and endless cosmic pillar (Stambha) of fire, the cause of all causes. Lord Shiva is pictured as emerging from the Lingam – the cosmic pillar of fire – proving his superiority over gods Brahma and Vishnu. This is known as Lingodbhava. The Linga Purana also supports this interpretation of lingam as a cosmic pillar, symbolizing the infinite nature of Shiva. According to Linga Purana, the lingam is a complete symbolic representation of the formless Universe Bearer - the oval shaped stone is resembling mark of the Universe and bottom base as the Supreme Power holding the entire Universe in it. Similar interpretation is also found in the Skanda Purana: "The endless sky (that great void which contains the entire universe) is the Linga, the Earth is its base. At the end of time the entire universe and all the Gods finally merge in the Linga itself."  In yogic lore, the linga is considered the first form to arise when creation occurs, and also the last form before the dissolution of creation. It is therefore seen as an access to Shiva or that which lies beyond physical creation.
During the creation a debate took place between the creator Brahma and the preserver Vishnu that who Shiva is. Just then this “Column of light” appeared in front of them on the Hindu month of Margasheersha and Hindu date Poornima or Pratipada. When both the Gods failed to know the real origin and end of this column, Shiva appeared in his visible form. He preached both of them the real meaning of Shiva Lingam.
He said, ” I have two form, Sakala(with form) and Nishkala(with out form). This column of light is my real form. Brahman is my Nishkala form and Maheshwara is my Sakala form.
When I come with sixteen kalas, I become Sakala and when I manifest in the crude energy, I am called Brahman. Brahman means the most enormous (Brihat) and the creator of all. Lingam depicts my formless Brahman power.
This is my Lingam (symbol). Lingam (Braman) and Lingee (आत्मा – Atman) are same, therefore the great souls should also worship me. One who has established Shiva Lingam somewhere in his life, he gets Sayujya Moksha (eternal company of Shiva).
From Vedanta :- A subtle representative of God that is present in our body. Kundalini is coiled with it in three and half coils. This is what Shiva Lingam and snake coiled round depict in our temples. It shows Paramatman in the form of Atman and Shakti in the form of Kundalini.
Let us know what Lingam means as per The Lingam Purana:
प्रधानं प्रकृतिर यदाहुर्लिगंउत्तम । गंध-वर्ण-रसहिंनं शब्द-स्पर्शादिवर्जितं ॥
Meaning: The foremost Lingam which is devoid of colour, taste, hearing, touch etc is spoken of as Prakriti or nature.
The nature itself is a Lingam (or symbol) of Shiva. When we see nature, we infer the presence of its creator – Shiva. Shiva Lingam is the mark of Shiva the creator, Shiva the sustainer and Shiva the destructor. It also dispels another myth in which Shiva is considered only as a destructor.
Another authentic reference comes from Skanda Purana where lingam is clearly indicated as the supreme Shiva from where the whole universe is created and where it finally submerge.
आकाशं लिंगमित्याहु: पृथ्वी तस्य पीठिका। आलय: सर्व देवानां लयनार्लिंगमुच्यते ॥ (स्कन्द पुराण)
Meaning: The endless sky (that great void which contains the entire universe) is the Linga, the Earth is its base. At the end of time the entire universe and all the Gods finally emerge in the Linga itself.
Forms of Shiva Lingam
Shiva Lingam is worshiped in two common forms – Chala (Moveable) Lingam and Achala (Non-Moveable or Fixed) Lingam. 
Anthropologist Christopher John Fuller conveys that although most sculpted images (murtis) are anthropomorphic, the aniconic Shiva Linga is an important exception. Some believe that linga-worship was a feature of indigenous Indian religion.
There is a hymn in the Atharvaveda which praises a pillar (Sanskrit: stambha), and this is one possible origin of linga-worship. Some associate Shiva-Linga with this Yupa-Stambha, the sacrificial post. In that hymn a description is found of the beginningless and endless Stambha or Skambha and it is shown that the said Skambha is put in place of the eternal Brahman. As afterwards the Yajna (sacrificial) fire, its smoke, ashes and flames, the soma plant and the ox that used to carry on its back the wood for the Vedic sacrifice gave place to the conceptions of the brightness of Shiva's body, his tawny matted-hair, his blue throat and the riding on the bull of the Shiva. The Yupa-Skambha gave place in time to the Shiva-Linga. In the Linga Purana the same hymn is expanded in the shape of stories, meant to establish the glory of the great Stambha and the supreme nature of Mahâdeva (the Great God, Shiva).
According to Shaiva Siddhanta, which was for many centuries the dominant school of Shaiva theology and liturgy across the Indian subcontinent (and beyond it in Cambodia), the linga is the ideal substrate in which the worshipper should install and worship the five-faced and ten-armed Sadāśiva, the form of Shiva who is the focal divinity of that school of Shaivism.
The oldest example of a lingam which is still used for worship is in Gudimallam. According to Klaus Klostermaier, it is clearly a phallic object, and dates to the 2nd century BC. A figure of Shiva is carved into the front of the lingam.
The lingam also figures importantly into various forms of Buddhism. Perhaps most notable is the use of penis images in the teaching of Drukpa Kunley, a Buddhist monk.
In 1825 Horace Hayman Wilson's work on the lingayat sect of South India attempted to refute British notions that the lingam graphically represented a human organ and that it aroused erotic emotions in its devotees.
Monier-Williams wrote in Brahmanism and Hinduism that the symbol of linga is "never in the mind of a Saiva (or Siva-worshipper) connected with indecent ideas, nor with sexual love." According to Jeaneane Fowler, the linga is "a phallic symbol which represents the potent energy which is manifest in the cosmos." Some scholars, such as David James Smith, believe that throughout its history the lingam has represented the phallus; others, such as N. Ramachandra Bhatt, believe the phallic interpretation to be a later addition. M. K. V. Narayan distinguishes the Siva-linga from anthropomorphic representations of Siva, and notes its absence from Vedic literature, and its interpretation as a phallus in Tantric sources.
Ramakrishna practiced Jivanta-linga-puja, or "worship of the living lingam". At the Paris Congress of the History of Religions in 1900, Ramakrishna's follower Swami Vivekananda argued that the Shiva-Linga had its origin in the idea of the Yupa-Stambha or Skambha—the sacrificial post, idealized in Vedic ritual as the symbol of the Eternal Brahman. This was in response to a paper read by Gustav Oppert, a German Orientalist, who traced the origin of the Shalagrama-Shila and the Shiva-Linga to phallicism. According to Vivekananda, the explanation of the Shalagrama-Shila as a phallic emblem was an imaginary invention. Vivekananda argued that the explanation of the Shiva-Linga as a phallic emblem was brought forward by the most thoughtless, and was forthcoming in India in her most degraded times, those of the downfall of Buddhism.
According to Swami Sivananda, the view that the Shiva lingam represents the phallus is a mistake; The same sentiments have also been expressed by H. H. Wilson in 1840. The novelist Christopher Isherwood also addresses the interpretation of the linga as a sex symbol. The Britannica encyclopedia entry on lingam also notes that the lingam is not considered to be a phallic symbol.
According to Hélène Brunner, the lines traced on the front side of the linga, which are prescribed in medieval manuals about temple foundation and are a feature even of modern sculptures, appear to be intended to suggest a stylised glans, and some features of the installation process seem intended to echo sexual congress. Scholars like S. N. Balagangadhara have disputed the sexual meaning of lingam.
Shivling (6543m) is also a mountain in Uttarakhand (the Garhwal region of Himalayas). It arises as a sheer pyramid above the snout of the Gangotri Glacier. The mountain resembles a Shiva linga when viewed from certain angles, especially when travelling or trekking from Gangotri to Gomukh as a part of a traditional Hindu pilgrimage.
Since the late 19th century some scholars have interpreted the lingam and the yoni to be representations of the male and female sexual organs. To practicing Hindus, however, the two together are a reminder that the male and female principles are inseparable and that they represent the totality of all existence.
But the basic and most common object of worship in Shiva shrines is the lingam.
. It was almost as if the linga had emerged to settle Brahma and Vishnu’s dispute. The linga rose way up into the sky and it seemed to have no beginning or end.
During September–October 1900, he [Vivekananda] was a delegate to the Religious Congress at Paris, though oddly, the organizers disallowed discussions on any particular religious tradition. It was rumoured that his had come about largely through the pressure of the Catholic Church, which worried over the 'damaging' effects of Oriental religion on the Christian mind. Ironically, this did not stop Western scholars from making surreptitious attacks on traditional Hinduism. Here, Vivekananda strongly contested the suggestion made by the German Indologist Gustav Oppert that the Shiva Linga and the Salagram Shila, stone icons representing the gods Shiva and Vishnu respectively, were actually crude remnants of phallic worship.
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