Answer
The ultimate purpose of Srila Prabhupada's appearance is the same as the ultimate purpose of Lord Krishna's appearance.
Krishna states in the Bhagavad-gita that He descends to this world to protect the devotees, annihilate the miscreants, and re-establish the eternal principles of religion (dharma). Srila Prabhupada came to continue that very same mission.
More importantly, Krishna has a confidential mission. He desires to reclaim all His eternal parts and parcels—the conditioned souls—by inviting them to surrender unto Him, take shelter of Him, become purified, and ultimately return to His eternal abode.
Krishna wants every living being to attain His personal association and engage in an eternal relationship of love with Him, where life is full of eternity, knowledge, and bliss.
This is Krishna's confidential purpose in appearing in this material world.
Srila Prabhupada came with that same confidential mission. Through the preaching of Krishna consciousness and the simple process of chanting the Hare Krishna maha-mantra, he sought to reclaim the suffering conditioned souls who have forgotten their eternal relationship with Krishna.
By sincerely chanting Hare Krishna, people gradually become purified, awaken their dormant Krishna consciousness, and prepare themselves to return to Krishna's eternal abode after giving up the present material body.
In Krishna's abode there is eternal life, full knowledge, and unlimited bliss. There are none of the defects, miseries, or limitations found in material existence. It is our real home.
Srila Prabhupada clearly expresses this purpose in the Introduction to the Bhagavad-gita As It Is, where he writes:
"Our only purpose is to present this Bhagavad-gita as it is in order to guide the conditioned student to the same purpose for which Krishna descends to this planet once in a day of Brahma, or every 8,600,000,000 years."
Thus, the purpose of Srila Prabhupada's mission is identical to Krishna's purpose.
Krishna comes to reclaim the conditioned souls who are suffering in forgetfulness of Him. He comes to revive their lost remembrance, awaken their Krishna consciousness, and prepare them to return to His eternal abode.
