In general, “Nightshades” are anything in the family Solanaceae. They contain neurotoxins for which most people naturally create an anti-toxin. Someone with a nightshade allergy doesn’t create the anti-toxin. The toxin then builds up in the body and causes an enormous amount of problems, which can differ from person to person, including mood swings, arthritis-like symptoms and inflammation, heart palpitations, digestive issues and more.
The problem is apparently alkaloids, like nicotine, atropine, capsaicin, solanine, tomatine.
(this is rather incomplete. I will update as time goes on!)