Your shadow once separated also leaves you with the inability to cast spells as seen with the Clockwork City Prologue. You can speak to the woman again in Arteaum and she tells you what it's like to live without a shadow. In the Summerset Trial, Cloudrest, if you or a group member dies in the battle with Z'Maja your shadow is ripped from your body and forced to fight your allies as a thrall under the Sea Sload.

As to what a Shadow is it seems to be the effect you leave on the universe and there is a whole line of magic dedicated to manipulating it. Shadow magic is very powerful and is mostly linked with Nocturnal and her followers, but some cunning mortals have been able to figure it out as well.

Can read more about it here.
https://en.uesp.net/wiki/Lore:Shadow_Magic

https://forums.elderscrollsonline.com/en-gb/discussion/577275/what-does-sotha-sil-mean-by-multiverse-in-the-summerset-chapter#latest in the neighboring topic also raised the issue of shadows, including the night blades, so you may be interested