Actually, in the US it's run at the state level. Each state has a "Grand Lodge", that issues charters for the local Lodges (and in some cases, owns the buildings). Each state "recognizes" other state Grand Lodges (and their local Lodges) as "regular"; this lets me go visit other Lodges that my state GL has recognition with, and so forth.
You might see lodges designated "AF&AM" or "F&AM" - that dates back to a minor schism long ago where you had the "Antient Free & Accepted Masons" vs the "Free & Accepted Masons" - all that boils down to these days is minor differences in ritual and ceremonies. That's one of the nice things about visiting lodges in other states - to see how they do things differently!
You'll also see "Prince Hall" lodges - these are the Masonic equivalent of Historically Black Colleges & Universities. Nowdays, a white man can join an PH lodge, a Black man can join an AF&AM lodge, and so forth - and one thing I'm glad to see recently in Texas is that while we've had "recognition" between PH & the AF&AM lodges for over a decade now, we finally have "visitation" - where I can sit in an official meeting at a PH Lodge without having to officially request a visit through the Texas GL, and so on and so forth. This is the way it should have been for a long time, but honestly it took waiting for a lot of old racist guys to die off before we got to this point. Some states still don't have full recognition/visitation between the two and it's really upsetting (mostly in the Deep South).
We're basically a fraternal society with some secrets (all of which you can find out with the right Google searches) - we're not a "Secret Society". A lot of the secrets are just passwords, modes of recognition, and so forth. Stuff that boils down to (in my opinion) "If you can't trust your Brother to keep these simple secrets, can you trust him with anything else?"
Shortest simplest explanation: a bunch of guys who hang out once or twice a week and have a fancy dress meeting once a month, to get away from the wives, have dinner, BS and catch up with each other, and do some good for the community in whatever ways we can. We're there for each other, and anyone else that might need help that we can provide. There's really no "secret advantage" to being a Mason that's different than having friends who own businesses in "normal life" - at one time I joked that my Masonic tattoo might get me a discount on an oil change and I could get cupcakes at wholesale...
There's no "Illuminati" or world-running society. How can you expect us to run the world when sometimes we can't even decide what to serve for dinner?
It's really no different than belonging to any other social organization. My Brethren kept me sane and alive after my wife passed away in 2009 - I'd be sitting here at home alone, would get a phone call. "Hey we're here at Lodge cooking for the meeting on Wednesday, want to come hang?" "Nah, I'm okay, thanks." Five minutes later the phone would ring. "Bill, this is the Worshipful Master, if you're not here in 15 minutes I'm sending a truck full of guys to haul your ass up here.." They knew I needed to be around other people and to be distracted. (the WM is basically the elected president of the lodge for each year)