The concept of the “Shadow Self” is a Carl Jung original, although I don’t care much for the background of anything I’m interested in, so that concludes your history lesson. Distilled gold or bust.
The “Shadow” is essentially what we, as humans, deny or reject in ourselves. The “bad” or “good” qualities that we revile or relish. The Shadow can be what doesn’t gain us acceptance, parts of ourselves we were told were nasty, or parts that got us the kind of attention we despise, and so we unceremoniously stuffed them into the Shadow. BUT It’s also what we idealize in others, as if it's something we are unable to access. This process is largely unconscious, as our ego automatically shoves what’s undesirable into the Shadow, and highlights what’s desirable (in whatever frame that manifests for you, personally).
Why would we push traits we admire in others into our shadow? We may have been shamed, humiliated, chastised, or put in other “dangerous” feeling situations as a result of those traits. Like if you have a fear of standing out it’s probably because something negative happened in your past as a result - like a pack of envious girls kicked you out of your friend group or your parent made you feel like shit.
When our shadow is activated by a person or situation, it can show up as “triggers”, bursts of reactivity or projections. We can feel immobilized by terror, envy, shame or anger. It can literally paralyze you, often pulsating out of your chest, rising up to your face in red hot heat… you go into fight or flight. Or sometimes on a lower level, it just shows up as being illogically reactive and hostile or overly annoyed at someone or some situation. But it’s often where our principles, ego and self-righteousness reside. The absolutely non-negotiable terrain that you firmly plant your feet in each and every single day.
You might encounter someone out in the wild, socially, or at work - and they rub you the wrong way. You end up stewing on what a piece of shit they are for hours, and how you can’t believe someone can behave in such an abhorrent way. However, it’s possible they’re simply reflecting your Shadow back at you.
The Shadow is what you deny about yourself, or simply deny yourself, and project onto others. Another way of looking at the Shadow is as your repressed “Id”; the urges, desires and impulses (both libidinal and destructive) that you stifle and deny expression. And the more you repress these urges and desires, the bigger the Shadow gets.