Bindumādhava is the main form of Bhagavān Vishṇu at Kāśī. He stays at the Pañcanada Tīrtha, which lies beside Maṇikarṇikā. Chapter 60 of the Kāśī Khaṇḍa (Uttarārdha) tells how Bhagavān Vishṇu chose to live at Pañcanada in preference to Vaikuṇṭha itself, and on what terms this dwelling blesses devotees.

In the four yugas he has different names: Ādimādhava in the Kṛta Yuga, Anantamādhava in the Tretā Yuga, Śrīmādhava in the Dvāpara Yuga and Bindumādhava in the Kali Yuga.

Origin of the name

The name Bindumādhava has two meanings.

Bindu, from Agnibindu. The ṛshi Agnibindu (whose name means “drop of fire”) did long tapas (austerity) at Pañcanada and pleased Bhagavān Vishṇu. When Bhagavān Vishṇu appeared and declared that he would stay there for ever, the “Bindu” of Agnibindu’s name became part of his own name.
Ma and dhava. “Ma” stands for Mahālakshmī (Śrī), and dhava means lord or husband. So Bindumādhava is both Agnibindu’s Mādhava and the dhava (master) of Lakshmī.

(Chapter 60)

Why Bhagavān Vishṇu prefers Kāśī to Vaikuṇṭha

Agnibindu asked Bhagavān Vishṇu to stay at Pañcanada for ever. Bhagavān Vishṇu agreed fully and said, “I prefer this tīrtha of Pañcanada to Vaikuṇṭha.”

At Vaikuṇṭha, Bhagavān Vishṇu gives sālokya (living in the same world as him), sārūpya (a form like his) or sāmīpya (nearness to him). But at Kāśī, under the highest rule of Viśveśvara, what is given is sāyujya: full merging into Brahman, the highest and last moksha (liberation). Here Bhagavān Vishṇu himself is under the rule of Bhagavān Śiva. Nearness to the direct grace of Bhagavān Śiva makes Kāśī greater even than Vaikuṇṭha for the devotees of Bhagavān Vishṇu. (Chapter 60)

The twenty-four mūrtis and the forms of Vishṇu

The Kāśī Khaṇḍa lists about thirty forms of Bhagavān Vishṇu present at Kāśī. The names given are Keśava, Madhuhā, Saṅkarshaṇa, Dāmodara, Vāmana, Pradyumna, Vishṇu, Mādhava, Aniruddha, Purushottama, Adhokshaja, Janārdana, Govinda, Trivikrama, Śrīdhara, Hṛshīkeśa, Narasiṃha, Achyuta, Vāsudeva, Padmanābha, Upendra, Hari and Kṛshṇa.

Each of the twenty-four forms goes with a particular arrangement of the four weapons: śaṅkha (conch), cakra (discus), gadā (mace) and padma (lotus). Each gives particular results. (Chapter 61)

Warning to devotees of Vishṇu who hate Viśveśvara

Bhagavān Vishṇu gave a clear warning at Pañcanada. Devotees of Bhagavān Vishṇu who hate Viśveśvara will become piśācas (ghosts) for thirty thousand years. These are people who see Bhagavān Śiva and Bhagavān Vishṇu as set against each other, not as one. Kāśī is called the Pāśupata-sthali, the holy field of devotion to Bhagavān Śiva. (Chapter 60)

Kārttika vrata at Bindumādhava

The Kāśī Khaṇḍa lays down a full Kārttika vrata (vow) at Bindumādhava. Through the whole month of Kārttika the devotee keeps celibacy, follows certain rules about food, keeps lamps burning before Bhagavān Vishṇu, and recites the Dāmodara mantra each day.

The month ends with Prabodhinī Ekādaśī, the bright Ekādaśī of Kārttika, also called Utthanā Ekādaśī, when Bhagavān Vishṇu wakes from his cosmic sleep. The devotee stays awake on the nights of Ekādaśī and Dvādaśī, worships Bhagavān Vishṇu at Bindumādhava, and feeds brāhmaṇas. By this the devotee never returns to earth. (Chapter 60)

Sources

Skanda Mahā Purāṇa, Kāśī Khaṇḍa, Chapters 60–61
Chapter 60: the origin of the name, Bhagavān Vishṇu’s choice of Pañcanada, the warning, and the Kārttika vrata
Chapter 61: the forms of Bhagavān Vishṇu at Kāśī