PRS or mechanical copyright protection society (MCPS) gives you permission for us to protect your rights and collect royalties on your behalf. When you join you have to register to be able to use the privileges provided by the PRS or MCPS.
Copyright is the legal right to owning something you made and in music, if you right or make a song you can have the rights to them and get royalties whenever that song is played or bought people like PRS and MCPS are the middlemen of this front if you give them the rights they will make sure you get paid whenever your song is broadcasted live via TV or radio and bought but of course the PRS and MCPS get there cut for doing their job and you might get the majority just not all of it.