In traditional Christianity the label "Christ" is applied to one man- the historical figure known as Jesus of Nazareth. It is a title used to depict his privileged status as the savior of mankind. In New Age thought the word Christ is generally not used to refer to a particular person, but is instead used to describe a state of consciousness called "Christ consciousness".
"Christ consciousness" is an exalted state of consciousness where the person experiences a sense of oneness with all creation. In this state it is impossible to do harm to another for that "other" is seen as part of one's own larger self. This state is in contrast to the "duality" state of consciousness, also called the fallen state, separation etc.
In the state of duality the person experiences themselves as fundamentally separate from the rest of creation and they believe they can harm another without harming themselves. This is the state many live in and according to certain spiritual teachings the spiritual path represents a movement from the state of duality to the state of oneness or Christ consciousness.
Christ consciousness is what is believed to be described in the famous quote of Jesus: "The kingdom of heaven is within". That is, the kingdom of heaven is a state of non-dual (unity) consciousness which is available to anyone who seeks it, without the need for an outer authority to grant it!