Sometimes the explanation is given that “Why we have got 108 beads?”
“Because there are 108 Upaniṣad.”
So chanting of Hare Kṛṣṇa with 108 beads means that we are surpassing the study of 108 Upaniṣads.
Another meaning is that there are 108 damsels who served Kṛṣṇa with all respect at Vṛndāvana. So that is also another explanation, 108. We are serving Kṛṣṇa’s servitors, hundred and…, chief damsels of…, at Vṛndāvana.
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According to the Muktikā Upaniṣad, there are 108 Upaniṣads. The 108 Upaniṣads contain all knowledge about the Absolute Truth.
Sometimes people ask why Vaiṣṇavas use 108 prayer beads for chanting the holy names. We think it is because there are 108 Upaniṣads containing full knowledge of the Absolute Truth.
On the other hand, some Vaiṣṇava transcendentalists think that the 108 beads represent the 108 companions of Lord Kṛṣṇa in His rāsa dance.
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Kṛṣṇa had many thousands of cows, and they were divided into groups according to their colors. They were also differently named according to color. When He would prepare to return from the pasturing ground, He would gather all the cows.
As Vaiṣṇavas count 108 beads, which represent the 108 individual gopīs, so Kṛṣṇa would also count on 108 beads to count the different groups of cows.
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The number 108 had a special significance: there were 108 Upaniṣads, as well as 108 principal gopīs, the chief devotees of Lord Kṛṣṇa.
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जपेदष्टोत्तरशतं स्तुवीत स्तुतिभि: प्रभुम् ।
कृत्वा प्रदक्षिणं भूमौ प्रणमेद् दण्डवन्मुदा ॥ ४२ ॥
japed aṣṭottara-śataṁ
stuvīta stutibhiḥ prabhum
kṛtvā pradakṣiṇaṁ bhūmau
praṇamed daṇḍavan mudā
Synonyms
japet — should silently murmur; aṣṭottara-śatam — 108 times; stuvīta — should offer prayers; stutibhiḥ — by various prayers of glorification; prabhum — unto the Lord; kṛtvā — thereafter doing; pradakṣiṇam — circumambulation; bhūmau — on the ground; praṇamet — should offer obeisances; daṇḍavat — straight, with the whole body; mudā — with great satisfaction.
Translation
Thereafter, one should silently murmur the mantra 108 times and offer prayers to the Lord for His glorification. Then one should circumambulate the Lord and finally, with great delight and satisfaction, offer obeisances, falling straight like a rod [daṇḍavat].
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Śrīla Jīva Gosvāmī has very nicely described this vasudeva, or śuddha-sattva, in his Bhagavat-sandarbha. He explains that aṣṭottara-śata (108) is added to the name of the spiritual master to indicate one who is situated in śuddha-sattva, or in the transcendental state of vasudeva.
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