Kailāsa is the divine mountain, the highest home of Bhagavān Śiva and Devī Pārvatī. The Brahma Vaivarta Purāṇa, Brahma Khaṇḍa, Chapter 25, says it lies one lakh yojanas above Dhruva, the pole star. It is one lakh yojanas wide. It holds three crore crystal mansions and four crore puṇyakshetras (holy places). It is free from disease, old age and death. Kailāsa is where Nārada met Bhagavān Śiva and received the teaching of the Āhnika, the code of daily conduct.

The Matsya Purāṇa, Chapter 120, describes Kailāsa on the earth, in the Himālaya.

Description in the Brahma Vaivarta Purāṇa

Chapter 25 of the Brahma Khaṇḍa gives these details:

Place: one lakh (100,000) yojanas above Dhruva, the pole star (Dhruvaloka).
Size: one lakh yojanas across.
Mansions: three crore (30,000,000) crystal mansions.
Holy places: four crore (40,000,000) puṇyakshetras.
Freedom from suffering: no vyādhi (disease), no jarā (old age), no mṛtyu (death).

Kailāsa is a realm beyond the three ordinary sorrows of mortal life, and Bhagavān Śiva’s divine retinue lives there.

Bhagavān Śiva on Kailāsa

When Nārada came to Kailāsa, he found Bhagavān Śiva repeating the name of Kṛshṇa (Kṛshṇa-nāmajapa) on a rosary of dark lotus (nīlotpala). Bhagavān Śiva is the lord of all jñāna (knowledge) and the greatest of the Vishṇu-bhaktas. Nārada was deeply moved to see him lost in the name of Kṛshṇa. Nārada sang a Kṛshṇa-stuti, a hymn of praise to Kṛshṇa. Bhagavān Śiva was glad, embraced Nārada warmly and gave him what he had come to seek. (Brahma Vaivarta Purāṇa, Brahma Khaṇḍa)

The Āhnika taught to Nārada

The main gift Bhagavān Śiva gave Nārada on Kailāsa was the Āhnika, the code of daily conduct for a devout person. Chapter 26 tells this teaching. It covers:

Brahmi-muhūrta practice: rising at brahmi-muhūrta and first meditating on the guru.
Mala-mūtra rules: twelve forbidden places, and the right directions for different times of day.
Śauca rules: the number of applications of mṛttikā (earth) for ritual purity.
Seasonal snāna rules: a different bathing rule for each of the six seasons.
Aśvakrānta mantra: the mantra for beginning the bath.
Saṃdhyāvandana: the practice three times a day, whose merit equals that of visiting all tīrthas.
Shoḍaśopacāra pūjā: the sixteen-step pūjā.
Śālagrāma worship: the rules for worshipping the Śālagrāma śilā.
Daily śrāddha: the daily rite for the ancestors.
Yajña: the place of the yajña in daily life.

(Brahma Vaivarta Purāṇa, Brahma Khaṇḍa, Chapter 26)

Kailāsa above Dhruvaloka

In this text Kailāsa is a realm above Dhruvaloka, free from suffering, filled with the divine retinue of Bhagavān Śiva. Bhagavān Śiva himself is found there repeating the name of Kṛshṇa, though he is the greatest of the Vishṇu-bhaktas.

Kailāsa in the Matsya Purāṇa

The Matsya Purāṇa, Chapter 120, describes the land around Kailāsa as part of its account of the Himālaya. Kailāsa lies north of the āśrama of Atri Muni, on the back (the northern side) of the Himālaya. It is the home of Bhagavān Śiva. It is also the seat of Kubera, who lives there with his yaksha gaṇas. The Mandākinī rises from Kailāsa. She is the divine form of Gaṅgā as she flows in the celestial and upper earthly realms.

The directions of Kailāsa

The Matsya Purāṇa maps the holy land around Kailāsa by directions. Each has its own mountain, lake, river and presiding being.

Northeast (Īśāna): The Saugandhika mountain and the Suvela mountain stand here. The Acchoda lake (Acchoda-hrada) lies in this direction, and from it the Acchodakā river rises. The Caitraratha vana (the celestial forest) is here, guarded by the yaksha Maṇibhadra.

Southeast (Āgneya): The Lohita mountain (the red mountain) lies here, and the Lohita lake (Lohita-hrada), from which the Lohita mahānada (the great red river) flows. The Aśoka vana (the forest of Aśoka trees) is here, under the yaksha Maṇidhara.

Southwest (Nairṛti): The Kakudmat mountain is in this direction, and the holy Mānasa lake (Mānasa-hrada). From Mānasa the Sarayū river rises and flows south through Bhārata Varsha. The Vaibhāja vana (the forest of Vaibhāja) is here, under the rākshasa Brahmadhānu.

West (Paścima): The Sarvaushadhi mountain (the mountain of all medicinal herbs) and the Aruna mountain, described as Bhagavān Śiva’s favourite, lie in the west. The Śrīloda lake is here. From it the Śailodā river rises and flows west. Scholars identify it with the Oxus, or Amu Darya, river.

North (Uttara): The Hiraṇyaśṛṅga mountain (the golden-peaked mountain) stands here, and the Bindu-sara, the holy lake where Bhagīratha did his great tapas (austerity) to bring Gaṅgā down to the earth.

(Matsya Purāṇa, Chapter 120)

The descent of Gaṅgā from Kailāsa

The Matsya Purāṇa tells that Bhagavān Śiva released Gaṅgā from his jaṭā (matted hair) after Bhagīratha’s tapas at Bindu-sara. She divided into seven streams. Three streams, Nalinī, Hlādinī and Pāvanī, flowed east. Three, Sītā, Cakshus and Sindhu, flowed west. The seventh, the Bhāgīrathī, was led south by Bhagīratha to purify the remains of his ancestors, and at last reached the ocean at Gaṅgā-sāgara-saṅgama. (Matsya Purāṇa, Chapter 120)

Sources

Brahma Vaivarta Mahā Purāṇa, Brahma Khaṇḍa, Chapters 25–26
Matsya Mahā Purāṇa, Chapter 120