This is the mission of Sri Caitanya Mahaprabhu, that you go and preach and make propaganda about krsna-upadesa. This is Krsna consciousness movement. We are teaching all our men how to spread krsna-upadesa, how to spread Krsna consciousness. Then anartha upasamam saksat. Then all the unwanted things he has contaminated will be finished. Then pure consciousness… Pure consciousness is Krsna consciousness. Pure consciousness means to understand that "I am very much intimately connected with Krsna as part and parcel." Just like my finger is very intimately connected with my body. Intimate… If there is little pain in the finger, I become so much disturbed because I have got intimate connection with this finger. Similarly, we have got intimate connection with Krsna, and we are fallen. Therefore Krsna also feels little pain, and therefore He comes down: paritranaya sadhunam vinasaya ca duskrtam dharma-samsthapanarthaya sambhavami yuge yuge [Bg. 4.8] Krsna is feeling pain. So you become Krsna conscious, then Krsna will feel pleasure. That is Krsna consciousness movement.
From Srila Prabhupada's lecture on Srimad-Bhagavatam 1.7.7 — Vrndavana, April 24, 1975