The Kinnaur Kailash (locally known as Kinner Kailash) is a mountain in the Kinnaur district of the Indian state Himachal Pradesh. The Kinnaur Kailash has a height of 6050 meters and is considered as sacred by both Hindu and Buddhist Kinnauris.

As per a legend the shrine of Kinnaur Kailash has been known to be present since the time of the deadly demon, Bhasmasur. Bhasmasur had got a blessing from Lord Shiva that anyone who touches the head of the demon will be turned to ashes. Bhasmasur upon seeing the powerful effects of this boon tried to bhasma Lord Shiva himself. It is this place where Lord Shiva hid himself in order to save himself. Lord Vishnu helped Lord Shiva by killing the demon.

The Kinner Kailash Shivlingam is a 79 foot vertical rock in the Kinner Kailash mountain range. On a clear day, one can see the Shivlingam which changes color during the course of the day. This Rock face is in between the 20,000 ft Kinner Kailash ranges of Mt. Kailash (19,850 ft) & Mt. Jorkanden (21,237 ft).

According to Hindu Mythology this is a very sacred place in the Indian Himalayas as it is associated with lord Shiva and Mata Parvati. A natural pond/Kund near Kinnar Kailash peak, known as Parvati Kund, is considered to be a creation of Goddess Parvati. She worshipped here for a long time. It is also the meeting place for Lord Shiva and Mata Parvati .

Mythology states that Lord Shiva conducted a meeting of Goddesses and Gods at Kinner Kailash peak every winter. This accounts for the Yatra that takes place every year during this time by devotees of Lord Shiva and local deities.

Source:

http://indiahikes.in/kinner-kailash-shivling-trek-diary/

https://en.wikipedia.org/wiki/Kinnaur_Kailash