In literature many terms like Christ consciousness, Krishna consciousness etc are used for a state of being attuned with God or super-consciousness where you are tuned to the infinite intelligence. Krishna consciousness is a state of being where you transcend the law of cause and effect which is ever operating and ever present. Every effect has a cause in the material world and by examining the cause, we can predict/understand the effects.
A Krishna conscious person is a person who transcends this law and is not affected by it in any way. This is the state of being that Krishna describes in Bhagvad Gita. He talks about not being affected by actions though performing them with our senses and mind. A Krishna conscious person is thus never affected by sorrow and misery that ordinary people of the material world experience. He doesn’t live in this world although being in a physical body. This is the spiritual kingdom that different religions describe.
Exact definition of Krishna consciousness would be the teachings of Bhagvad Gita where Krishna describes that a person although killing is not affected by the sin of killing. He asks Arjuna to rise above his ordinary state of being to Krishna consciousness and perform his duties of a warrior. In this state of consciousness, Arjuna although killing members of his own family would remain untouched by the sinful reactions.