Christ Consciousness has a double meaning, it is a state of Consciousness and also the Holy Spirit within you.
Christ Consciousness is a state of 'Enlightenment', in Buddhism called 'Nirvana', wich is the highest state of Enlightenment.
Christ Consciousness is the same as 'Buddha Consciousness, Krishna Consciousness or God Consciousness.
If someone has reached Christ Consciousness one lives in harmony with himself and his environment.
An enlightened person understand every situation and act on it from unconditional love.
It means also end of suffering; well, you can suffer but because you act from unconditional love your karma will stay clean and positive.
The other meaning is The Holy Spirit within you: the Spirit of Christ.
How to achieve Christ Consciousness/Nirvana?