The purpose of copyright is to allow anyone to own 'intellectual property' just as they own physical stuff. So just as you get to say who can play with your ball, you get to say who can perform, record or broadcast your music. And just as you could say, “I'll let you play with my ball for a dollar”, you can demand a payment whenever someone wants to use your music.
This is great so long as it works. But – continuing my analogy – what happens when someone steals your ball? They get to play with it, but you don't get any payment. That can happen with music. Someone hears one of your songs, likes it, and steals the tune to use in their own song. It's your tune, you created it, but now someone else is making money out of it. And worse still, they are saying it's their tune.
So just like it was your ball, it was your copyright. Someone stole your ball, someone infringed your copyright. You need to protect yourself.
So you go up to the guy who stole your ball and ask for it back. But he says, “It's not your ball, it's my ball!”. Likewise the person who stole your tune will say it's his tune and not yours. So just like you would have to prove that the ball is yours, you have to be able to prove that you wrote the tune.
The only way to prove authorship of a tune is to have some way of demonstrating that you wrote it on a certain date. If you can do that, no one who first heard the tune on any later date will be able to contradict the fact that you wrote it. So how can you do this?
The traditional way of protecting your copyright in this way is to make a copy of your song, either written or recorded, and mail it to yourself using signed-for delivery. Make sure you get a nice clear date stamp at the post office. When you receive the package, don't open it but keep it safe somewhere. One day, you might need to open the package in court, which will prove your authorship of the song. (In the US, you should also register your song with the Library of Congress, which you will need to have done to bring about a court action).
Well that's the theory. But in practice, these disputes rarely get to court. When they do, it nearly always turns out that whoever has the most money wins, regardless of the rights and wrongs of the case. That's just a fact of life in the music business, and it's not going to change any time soon.
In reality, you will be far better off simply getting on with writing music and getting it out there. The more people hear your music, the better your chances of success. OK, the better your chances of getting ripped off too, but that comes with the territory. Mailing your song to yourself however is so easy, there is no reason not to do it.
Just in case…