Lingam is the Sanskrit word for the male sexual organ (pronounced LING-AHM), loosely translated as "wand of light."  It's meaning is different in intention from the typical Western view of the penis.   In India, the lingam is respectfully viewed and honored as a "wand of light" that channels creative energy and pleasure.
 Perhaps the most famous lingam in the world is the Washington Monument which is an oversize copy an Egyptian obelisk. The ancient Egyptians believed that the spirit of the Egyptian Sun god, Ra - who represented the ultimate in masculinity and power - resided within the obelisk.

The sex act between male and female is represented by an lingam within a circle 
(yoni).  The Washington Monument sits within a circle.

Lingams polished and ready for sale
Natural lingams are found in Northern India where, 100,000 thousand years ago, a meteorite crashed and melded with the native rock. After thousands of years of washing and rolling in the flowing stream, many come shaped as you see above. Once a year the choicest stones are gathered by a special group of individuals.

Though it can be used as a technical term for the male phallus, specifically  lingam is term of reverence for the statues and images of the god Shiva’s genital organ. The thousands of lingams one finds throughout India and Nepal on almost every street corner and in every village square are worshipped even today as sacred symbols of Shiva (the "Destroyer" aspect in the all-male Vedic trinity).  People kiss and touch the statues, which are generally sculpted from stone; they offer rice, flowers, or fruit to them and will often color them with red ocher.

The Gupta-sadhana Tantra states that "infinite result is obtained by worship of a Sivalinga that should be made of crystal and other materials, but never of clay"