Prabhupada: Vande means "offering my respectful obeisances." Aham means "I." Vande 'ham sri-gurun, all the gurus, or spiritual masters. The offering of respect direct to the spiritual master means offering respect to all the previous acaryas. Sri-yuta means "with all glories, with all opulence." Pada-kamalam, "lotus feet." Offering of respect to the superior begins from the feet, and blessing begins from the head. The disciple offers his respect by touching the lotus feet of the spiritual master, and the spiritual master blesses the disciple by touching his head. Therefore it is said, "I offer my respectful obeisances unto the lotus feet of all the acaryas." Sri-gurun vaishnavams ca. Gurun means spiritual master, and vaishnavams ca means all their followers, devotees of Lord.
Spiritual master means they must have many followers. They are all Vaishnavas. They are called Prabhus, and the spiritual master is called Prabhupada because on his lotus feet there are many Prabhus. Pada means lotus foot. Not that the spiritual master alone, but along with his associates. And these associates are all Vaishnavas, his disciples. They are also devotees of the Lord; therefore they should also be offered respectful obeisances. Then sri-rupam. The spiritual master is descending from the Six Gosvamis. Out of the Six Gosvamis, Sri Rupa Gosvami and his elder brother Sanatana Gosvami are heading the list. Agrajatam means his elder brother, eldest brother. Sri-rupam sagrajatam saha-gana-raghunathanvitam. They are also associated with other Gosvamis, two Raghunathas, Raghunatha dasa Gosvami and Raghunatha Bhatta Gosvami. Then Sri Jiva Gosvami. So they are all offered respected obeisances one after another.
And after finishing respectful obeisances to the spiritual master and the Gosvamis, then we approach Lord Caitanya. Lord Caitanya is also approached with His associates. Savadhutam, sadvaitam. Sa means "with." Advaita, Advaita Gosai. And avadhuta means Nityananda. So with Advaita and with Nityananda, the offering goes to the Lord, Sri Caitanya Mahaprabhu. Then sri-radha-krishna-padan, then we approach Radha and Krishna. Radha-Krishna is also associate. We cannot approach Radha-Krishna directly. We have to approach through the spiritual master, through the Gosvamis, through the associates of Lord Caitanya. Then we approach Radha, then Krishna. If one approaches Krishna through this channel of disciplic succession, his efforts becomes successful. Otherwise, if he wants to approach Krishna directly, it will be futile endeavor.