"Or so they say" means "at least that is what other people say, but I don't know if that's true." It's a way to show that you are not agreeing or disagreeing with the statement. "Drinking tea with lemon will protect you from catching a cold, or so they say." "or so" by itself doesn't mean the same thing. It CAN mean "about". "Can you lend me five dollars or so? I want to get some lunch." It depends more on the situation. "We'd like to see the profits increase by 25% or so in the next year."

"or so they say" means like "That's what everyone else says" or "I think that's what other people think" Sometimes when you use "~Or so they say" you haven't REALLY HEARD people SAY that, you just assume they think that way.

The easy answer is: "Or so they say" means > I understand this is how most people describe me/it. (may or may not be true) Example: I'm not very good at math, or so they say. Means: I'm not very good at math. This is what I've been told or heard about myself (what other people think about my ability).

"Or so they say" means "so I hear", "so I'm told", or even simply "apparently". It's not a definite fact you're stating, just an opinion. "Or so they say" is used to make this more evident. "I'm not much of a romantic, apparently". You don't literally need a second opinion to use "or so they say".