The Legend about the importance of Amarnath Cave is as follows
This is The Cave which was chosen by "Bhole Shankar" for narrating the secrets of immortality and creation of Universe to Maa Parvati ji.
The Amar Kathaa of Shree Amarnath Ji
Centuries ago Maa Parvati asked Shiv ji to let her know why and when He started wearing the beads of heads ( Mund Mala) . Bhole Shankar replied when ever you are born I add one more head in my beads . Maa Parvati said ," 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".
Bhole Shankar replied that it is due to Amar Katha
Maa Parvati insisted that she may be told that secret. For long Shiva ji continued postponing . Finally on consistent demand from Maa Parvati He made up his mind to tell the immortal secret . He started for lonely place where no living being could listen it . He choose Amarnath Cave . In preparation to that He left His Nandi (The Bull which He used to ride) at Pahalgam (formar name Bail Gaon) . At Chandanwari He released Moon from his hairs (Jataon). At the banks of Lake Sheshnag He released the snakes . He decided to leave his Son Ganesha at Mahagunas Parvat (Mahaganesh Hill) .