The Shadow is a term used by psychotheorist Carl Jung to mean the perceptions, feelings, motives, beliefs, judgements, etc., about ourselves that are unconscious, repressed or undeveloped.
Shadow qualities—positive or negative—tend to be projected onto other people and external situations. The shadow is like a psychological blind spot, since we usually don't know these issues are there until we develop self-awareness.
For example, we might become attracted to someone who is confident, in part because we feel we lack confidence and we admire theirs. Yet, by the same token, we might also be annoyed by someone who is confident, perhaps because we feel dominated by their confidence and are unable to own our own confidence to stand up to theirs. In both cases, the more we become aware of the shadow dynamic and the more we learn to own the shadow issue, we may find that our feelings about that person changes.
In astrology, the planetary energies that we are unwilling, unable, or not ready to own and embrace tend to come back to us through external circumstances, situations and people. Self-awareness is the key that can open the door to illuminate our shadow. By discovering who we are, including (especially!) the parts of ourselves that we feel uncomfortable with (and therefore hide in our subconscious), we can begin to heal our hidden wounds and embrace self-acceptance.
The shadow can be represented by any planet, sign, house or aspect. However, these unconscious issues may be especially activated, in the natal chart or through transits involving, the opposition aspect, Scorpio, Pisces, 8th house, 12th house, Neptune, Pluto, or the Moon.
The psychological shadow is totally different from and not to be confused with the retrograde shadow.