Krsna consciousness means, "I am Krsna's," that's all.

Krsna says, mamaivamsah: "All these living entities, they are My part and parcel." So you have to understand this relationship with Krsna, that you are Krsna's. And Krsna, what is Krsna? Bhagavan.

From Srila Prabhupada's lecture on Bhagavad-gita 16.1-3 — January 29, 1975, Honolulu