One of the things Jung is known for is his theory of archetypes: personality types, roles, narrative modes, etc. Whereas Freud collected data clinically from his patients, Jung incorporated a system of archetypes and symbols from history, literature, and myth, thus combining archetypes similar to mythology and even metaphors. Corresponding to the traditional systems of Western thought, Jung also incorporated the binary (dualities and opposites) to describe his terms (i. e. conscious and subconscious). Jung suggests that these archetypes are located in the collective unconscious. And following the binary program, Jung speaks of a personal unconscious and a broader collective unconscious.
In Freud, the shadow could be equated with the entire personal subconscious or unconscious. In Jung, the shadow is located in both: personal and collective unconscious. It should be understood as a kind of psychic energy often associated with negative, evil, or abnormal thoughts, behavior, etc. Jung says that an individual psyche emerges and that individuation is successful if the individual is able to balance and/or manage the binaries of his/her self: conscious/unconscious and ego/shadow. We might consider the shadow(s) as those things we have repressed or things we know but do not want to admit about ourselves. Therefore, to correct some unconscious (shadowy) aspect, we must be conscious about that unconscious shadow. (This could be done individually but might require therapy, which could include dream analysis.) In "Psychology and Religion," he notes:
Unfortunately there can be no doubt that man is, on the whole, less good than he imagines himself or wants to be. Everyone carries a shadow, and the less it is embodied in the individual's conscious life, the blacker and denser it is. If an inferiority is conscious, one always has a chance to correct it.
The shadow refers to personal demons so to speak but in much larger in terms of Jung's broad, mystical or historical, schema of collective unconscious. The archetypes of the collective unconscious are recorded and re-performed - going all the way back to primitive times. Therefore, in Jung's thinking, the notion of the shadow has always been part of the collective and personal unconscious. The shadow is often associated with the negative aspects lodged in the personal and collective unconscious. The individual can correct any conflicts between the shadow and the conscious ego by consciously engaging and/or getting to the bottom causes, impulses, etc. that the shadow implies.