Reputation was what the forum used to use before XP and Laughs. I'm not sure how I got reputation since I joined longer after XP/Laughs were a thing. Also, when I click on it in the notification link, it takes me to a list of subscribed posts.
It seems to be some bug, a vestigial remainder of an older version of the forum.
You just have to learn to ignore it and hope it is fixed someday.
The website seems to handle notifications fine for me but the mobile app just does whatever it wants. It doesn't usually show the app badge icon on my phone's home screen unless I really have something, but within the app it pretty much always does. It shows I have PMs that I can't see (and don't really think exist), and often just randomly notifies me of thread updates that've I long since seen as if they were new. It's annoyingly as hell, but out of necessity I've learned to tune it out.