What is Shiva Lingam:
In Sanskrit, Linga means a “mark” or a symbol, which points to an inference. Thus the Shiva Linga is a symbol of Lord Shiva: a mark that reminds of the Omnipotent Lord, which is formless. Shiva Lingam is only the outward symbol of the formless being, Lord Shiva, who is the undying soul seated in the chambers of your heart. He is innermost self or Atman, and who is identical with the supreme Brahman.
A Shiva Lingam consists of three parts.
The typically circular base or peetham (Brahma-Pitha) holds an elongated bowl-like structure (Vishnu-Pitha) reminiscent of a flat teapot with a spout that has had the top cut off. Within the bowl rests a tall cylinder with a rounded head (Shiva-Pitha).
Nandi, the bull is depicted facing the sanctum in all Saivite temples, symbolizing Jeevatma (the human soul) yearning for realizing its oneness with Paramatma (the ultimate reality). 
Significance of Shiva Lingam
SHIVA, THE MAHAKAAL (PART–1)
Who is Shiva:
In Hinduism, Shiva is worshipped throughout India and a few other countries as one of the most important deity. Shiva is prayed in both forms viz. “saakar form” (as Lord Shiva or Shanker in form of deity) and Nirakar (as Lingam, formless). Shiva literally means “auspiciousness, welfare”. He is represented as god of destruction as destruction is root of re-creation (rebirth).
Saakar form of Shiva :
Shiva is depicted as under: