The episode in the Bhagwatam where Sri Krshna subdues Kaliya is of tremendous spiritual importance in the sadhana of Vaishnavism. While there is a historical significance to the stories, for a sadhaka the spiritual metaphors in each of these stories are of greater importance in the fullfilment of sadhana. Yamuna is the river of Bhakti or Chandra-nadi inside the human mind-body. Bhakti works best when it remains unpolluted by selfishness or a desire for gain. Even the slightest amount of personal desire corrupts the effect of Bhakti and produces no result. In its highest form devotion to the Supreme should be free from all calculations or sense of transaction – i.e. hoping for a gain in exchange for sadhana.
Kaliya corrupts the river of devotion using the poison of desire and the residents of Braj, devotees and lovers of God, are unable to enter into that perverted form of emotion. That is when Krshna enters into the dark waters of the Yamuna and subdues Kaliya, frees the heart from its natural cunningness and possessiveness and jealousy. And only then is the sadhaka able to experience a state of bliss which is the dance of Krshna.
This incident has also been used in some traditions as a protection against ill-effects of Naga-s and snakes. There were mantras aimed to harness the spiritual energy of this episode in Krshna’s Divine play, which it is believed can save a man in times of physical threat due to attacks from entities of the Naga loka. Even meditating on this image of Krshna can cause tremendous inner purification of the seeker and bring him closer to the experience of the Divine in the heart.
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mam paripalaya kaliya-ganjanaO Lord who playfully broke the yamala-arjuna trees, O Lord whose charming pastimes please everyone, O Lord whose dancing eyebrows defeat the restless khanjana birds, O conqueror of Kaliya, please protect me. (Mukunda-muktavali)
