Carl Jung defined "Shadow" as aspects of personality that your "ego" does not claim to be part of your self, the traits you do not want to own in yourself.
Like the times when you suddenly got into a bout of jealousy and anger only to later realize that, that is not who you are - you are not like that, then how come you experienced such jealousy and anger...
Or the time when we turned mean and nasty even though that went against your every grain of salt because you consider yourself to be kind and compassionate...
Or the time when you were wild and uninhibited only to later feel guilt and shame around your acts during the moments you were wild and uninhibited...
The way this begins is you make up a story of who you are supposed to be, how you are supposed to be, what you are supposed to do (and their respective nots). These stories are built up over a lifetime of your experiences since your childhood.
And then there are moments when life takes you through a journey of feelings and actions which do not fit your version of your story. And you do not like it. Your ego does not like it. So it makes up another story - that this is not who you are, how you are; This isn't you.
And In that moment you have given birth to a shadow aspect of your personality - the part of your personality that you do not accept as you.
And in doing so - you have fragmented yourself, your personality, your identity, your sense of who you are. These fragments lead you to feel incomplete because these fragments deny you the sense of yourself as a whole person. Rather you become "Parts" and not the "Whole". The more these shadows, these fragmented parts, the more conflict you experience within yourself and do not find the peace within.
To find that inner peace within, you need to become "Whole" again, you need to integrate all your fragmented personalities into your sense of wholeness and this begins only when you begin to accept these shadows as also being you. This is not easy work. Shadow integration can bring up a lot of disturbance that has got stored and repressed within - at the same, the only way to that inner peace is through this disturbance, through the acceptance.
There's a process called "Parts Integration" within the field of NLP that is designed to make this journey a lot easier although I must admit that when I did work with this process in the early days, I had limited knowledge of Shadows and hence my use of this process was limited to using it for decision dilemmas. Having known what I know today - I believe that Parts Integration is a very powerful tool to lead you to your Emotional Healing.
Wishing you a marvelous & beautiful relationship & an outstanding & fulfilling life.