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.
Śrīla Prabhupāda's lecture on Śrī Caitanya-caritāmṛta, Ādi-līlā 7.108 — February 18, 1967, San Francisco