THIS IS NOT A SINGLE ORGANISATION. IT IS A GENERIC TERM FOR ALL COLLECTING SOCIETIES.
A Collecting Society is an organisation which collects royalties on behalf of artists and performers. They are not content owners.
Organisations like ASCAP, BMI, GEMA, PRS and so on are collecting societies.
This is related to copyright, but isn't the same thing: we're talking here about performance and broadcasting rights. Basically, if you publicly perform or broadcast any music or virtually any sort, some sort of fee has to be paid. The exact rules vary from country to country, and very often royalties are payable on performances you wouldn't expect, sometimes even things that you would think were public domain. Quite often, even the composers and performers don't have much say in the matter and local collecting societies are authorized to collect fees for pretty much every public performance even if the artists don't see a penny of it. Sometimes it can get ludicrous: in Britain, one shopkeeper was once threatened with a massive fine because she would sing while she was working and this was deemed a public performance (the PRS backed down eventually).
Here's the important thing to understand, and why this is a case of "bad messaging": Whatever it looks like YOU ARE NOT BEING ACCUSED OF COPYRIGHT INFRINGEMENT. You are not being accused of anything. What this is is a notification that certain collecting societies are receiving royalties for broadcasts of your video.
How do these societies collect royalties? Two possible ways:
1. a "per performance" fee; or
2. a flat rate licence.
Here's the next thing to understand: THE PAYMENT OF ROYALTIES IS NOT YOUR CONCERN. If you have a live band and you perform at a concert hall, the concert hall will usually be licenced for any public performances of music. You don't need to worry: the organisers of the concert hall pay several thousand dollars per year for this licence (and part of the cost of booking the venue goes to pay for the licence), so it's taken care of.
It's the same on YouTube: You don't need to worry about getting a broadcasting licence, because YouTube has taken care of that on your behalf.
It may be that some collecting societies might want to be paid on a "per view" basis. If that's the case, then they would need to track videos that use content on which royalties are payable. As I understand it, then, this is just formal notification that your video is being tracked for the purposes of royalty payments.
