It means you like to watch them play?
Even if you are a "local" supporter - say you live in Wolverhampton and you support Wolves - even then, what "connection" do you have to the club? What actual difference does it make to your life whether they win a match or lose it? None whatsoever. So then what does it mean to be a fan or follower?
It just means you like to watch them play, and have watched them for long enough that you know more about that club, and take a greater interest in what's going on with it. Whether their home ground is physically located 1 mile or 20 miles away from my house seems to be quite inconsequential.
I've always wondered this about die hard, "local" supporters: Suppose hypothetically, all of the players from your local club got bought by Barcelona in the next transfer window, and all of the players from Barcelona got bought by your local club. And the managers and coaching staff etc. swapped jobs as well. Who would you support now?
If you're still supporting your "local" club after this - then what exactly is it that you have a "connection" with? Just the name of the club? Just the colour of their shirts? Just the fact that the stadium is located in your area? All the players have left, they've taken their style and quality of football with them. So it's not really about the football anymore, is it? This isn't really being a
football fan.
And if you decide to support Barcelona now, because that's where all your favourite players have gone - then you're not really a "local" supporter at all, are you? Because what keeps you supporting your club is not the fact that they're local to you, but it's the fact that you like those players, and their style/quality of football. And if that's the case, it should be easy to understand why some people support the "big" clubs even if they're not local.
I don't really know why this debate keeps coming up anyway though. What difference does it make to you (or anyone) what club someone else supports, or on what basis they choose to do so? Why can't everyone just support whatever club they want, for whatever reason they want, and just leave it at that? Why should anyone have to justify what team they like to watch, and want to win?