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 class on Srimad-Bhagavatam 1.7.7 — Vrndavana, April 24, 1975)