I just see the term to mean the opposite of specialist, or someone who is passionate about the topic.
In internet terms, it generally means not a geek.
It’s a good distinction, because for geeks, internet is something inherently interesting on a technological and philosophical level. For, well, normies, it’s just an appliance they don’t need to know much about.
Similarly if you go to a car show but don’t really know shit about cars other than they have 4 wheels, you’re a normie in that environment. Your requirements on what a car should be like, are fundamentally different from someone who likes to tweak and tinker.
I wish the term could just mean that without any negative connotations, because I don’t see anything wrong with that distinction.
Ed/add: Nobody can know everything about every topic, so everyone is a normie in some category. Usually without realising it. So that’s just it. Not necessarily an insult, and doesn’t even make much sense as one, I think.