Translation: By the mercy of Vyasa, I have heard these most confidential talks directly from the master of all mysticism, Krishna, who was speaking personally to Arjuna.
Explanation: The Bhagavad-gita is actually a set of nested conversations being transparently relayed by the pure devotees of the Lord. At the inner core is the sacred conversation between Krishna and Arjuna. This was being heard and relayed by Sanjaya to Dhrtarastra. This conversation is being relayed to us by Srila Vyasa-deva.
In the previous verse Sanjaya had acknowledged the potency of the message he has heard. Just as Arjuna had thanked Krishna for removing his illusion, Sanjaya immediately thanks his guru, Vyasadeva, for empowering him to listen to this sacred conversation. The spiritual master is the transparent media by which a disciple can understand the science of god consciousness. Srila Prabhupada calls this the, "the mystery of the disciplic succession." Even though Sanjaya is happy that he has heard the message directly from the supreme mystic Krishna, he also acknowledges that it is only possible by the mercy of his guru, Vyasadeva.
A bona-fide spiritual master must appear in a recognized disciplic succession. There are four recognized vaishnava sampradayas coming dowm form the four prominent devotees of Lord Krishna, Brahma-sampradaya comes down from Lord Brahma; Sri-sampradaya comes from Goddess Lakshmi; Rudra-sampradaya from Lord Shiva; and Kumar-sampradaya from the four Kumar sons of Lord Brahma. Unless a guru is linked to one of these disciplic successions, he cannot make a claim to be authentic. Sanjaya was the disciple of Vyasadeva, who was the disciple of Narada, who was the disciple of Lord Brahma. Thus he was in the Brahma-sampradaya. In each sampradaya there appeared a prominent acarya who has made it famous. In Brahma-sampradaya it is Sri Madavacarya. In Sri-sampradaya it is Sripada Ramanujacarya. In Rurdra-sampradaya it is Vishnujana Swami and in Kumar-sampradaya it is Nimbarakacarya.
In the Brahma-sampradaya, Krishna appeared Himself as Caitanya Mahaprabhu. He further adorned the sampradaya by taking and emphasizing two things from each of the four sampradaya acaryas. From Madhavacarya of Brahma-sampradaya: the complete defeat of impersonalist Mayavada philosophy [kevale-advaita-nirasana], and service to the Deity of Krishna by accepting the Deity as an eternal spiritual being [krsna-murti-sevana]. From Ramunjacarya of Sri-sampradaya: the concept of bhakti unpolluted by karma and jnana [ananya-bhakti], and service to the devotees [bhakta-jana-seva]. From Vishnujana Swami of Kumar-sampradaya: teaching the sentiment of exclusive dependence on Krishna [tadiya-sarvasva-bhava], and the path of raga-bhakti [raga-marga]. From Nimbarkacarya of Kumar-sampradaya, the necessity of taking shelter of Radha [ekanta-radhikasraya], and the high esteem for the gopis' love of Krishna [gopi-bhava].
Srila Prabhupada, the founder acarya of ISKCON appears in direct disciplic succession of Lord Caitanya Mahaprabhu. ISKCON is therefore considered to be in the Brahma-Madhava-Gaudiya sampradaya. Srila Prabhupada comments, "In Bhagavad-gita, all the yoga systems--karma-yoga, jnana-yoga and bhakti-yoga--are explained. Krishna is the master of all such mysticism. It is to be understood, however, that as Arjuna was fortunate enough to understand Krishna directly, so, by the grace of Vyasa, Sanjaya was also able to hear Krishna directly. Actually there is no difference between hearing directly from Krishna and hearing directly from Krishna via a bona fide spiritual master like Vyasa. The spiritual master is the representative of Vyasadeva also. Therefore, according to the Vedic system, on the birthday of the spiritual master the disciples conduct the ceremony called Vyasa-puja.