Actually, you read it wrong... it doesn't influence... however, reputation does influence some things.
For example, it influences the amount of followers you get. I've noticed there are certain people who only bother to comment, vote and follow if a user has 60+ in Reputation... others 50+.
They think that's where the money lies, so they have to follow the money... They are wrong, but it's a fact that the higher the rep the better you tend to do.
Oh, maybe I shouldn't be reading posts on zero sleep lol. Oh that makes sense! Thanks for explaining. Yeah, they're wrong. My reputation is getting pretty good since I only did my first intro post on Feb 1, but my votes are only worth point .08 at full power. That's ok... They'll grow 😀.