Amarrnath cave is a Hindu shrine located in Jammu and Kashmir, India. It is dedicated to Shiva. 
The Amarnath cave is situated at an altitude of 3,888 m (12,756 ft) about 141 km (88 mi) from Srinagar, the summer capital of Jammu and Kashmir.Pilgrims visit the holy site during the 45-day season around the festival of Shravani Mela in July - August, coinciding with the Hindu holy month of Shraavana. This whole yatra and the Shrine is managed by Shri Amarnathji Shrine Board (SASB), that was constituted by an Act of the Jammu & Kashmir State Legislature.

AMARNATHJI STORY

The Story Of Amarnath Ji
The story begins from the quest of Goddess Parvati when she asks her husband Lord Shiva to tell her why he wore a Maala with Munds (Mund Maala - bead of heads). Lord Shiva replies that every time she(Parvati) is born, he adds a head to the Maala he is wearing.
Parvati enquires, "My Lord, my body is destroyed every time and I die again and again, but you are Immortal. Please let me know the secret of this." Lord Shiva replies that he is immortal due to Amar Katha and whoever knows that Katha becomes Immortal. When Goddess Parvati insists on knowing the story then Lord Shiva explains to her that this story is a secret and no one knows this and even Gods do not know about this story and hence, when their virtues are over, they have to leave their position and take rebirth to gain virtues. It is only the Tridevs (Brahma, Vishnu and Mahesh) that know this sacred story and are immortal. 

But when Parvati insists more vehemently, Lord Shiva assures her of telling the Amar Katha sometime. But the goddess does not let go and on her persistent demand to know the secret of Immortality, Lord Shiva selects a hidden place (Amarnath Cave) where no living being could listen to this secret story.

On way to Amarnath Cave, Lord Shiva leaves Nandi, The Bull, at Pahalgam (Bail Gaon). At Chandanwari, he releases the Moon from his hair (Jataon). On the banks of Lake Sheshnag, he releases his snakes. At Mahagunas Parvat (Mahaganesh Mountain), he leaves his son, Lord Ganesha. At Panjtarni, Lord Shiva leaves behind the five elements- Earth, Water, Air, Fire and Sky. As a symbol of sacrificing the earthly world, Lord Shiva performed the Tandava Dance. Then, finally, Lord Shiva entered the Holy Amarnath Cave along with Parvati. Lord Shiva then took his Samadhi on the Deer Skin. 

Lord Shiva started telling the story to Mata Parvati but she sleeps in between as the story was very long and she was tired of the journey. Meanwhile, two white pigeons were listening to the story and were making cooing sound which made Shiva feel that Mata Parvati is still listening to the story and he continued telling it. In this way, both the Pigeons heard the story of being immortal.
After ending the story, when Lord Shiva saw that Parvati was sleeping, He wondered who was making the cooing sounds when he was narrating the story. He then discovered the two pigeons and became angry and tried to kill them but the pigeons said that if you will kill us then the legend of this story shall exist no more. Then Lord Shiva left them alive and blessed that they will reside at this place as a symbol of Lord Shiv and Goddess Parvati. It is said that even today the devotees often see a pair of pigeons here.

It is said that only those reach Amarnath Dham who are blessed by Baba Bhole Nath. Even reaching here is a great virtue. Person sighting and worshipping Baba Himani reaches heaven after this mortal life.