It is not penis. The story behind Shiv ling goes like this,Once Lord Brahma and Lord Vishnu were in a heated argument about who is superior. They went to Lord Shiva to solve their dispute. Shiva told them that he would manifest as a large beam of light and the one who returns after seeing the end of the beam would be superior. They accepted the challenge. One of them headed towards the top of the beam and the other to the bottom. They traveled along the beam hoping to see its end but in vain. The beam seemed to grow as they traveled further. Neither of them reached the end of the beam . However, lord Brahma returned and lied that he reached the end of the beam which was a false claim and Shiva knew it. Shiva cursed Brahma for lying that he wouldn't be worshiped by anyone on earth. This beam form of Lord Shiva is worshiped as Shiva linga.
Lord Shiva With Mata Parvati
Lord Shiva Stories