As far as the About section helps me, it seems that you share your Amplify page with all your listeners, and if you get x number of views, or "Amplifies," your song is sent to a group of higher-ranking music moguls, or already-famous musicians, one or the other. Either way, it vastly increases your chances of being noticed by someone who can change your life, basically. The "Amplifies" thing is just a firewall to keep out all the n00bs with less than ten fans on Facebook, I think. They want serious people for this. But I'm just informing you guys, I don't claim that this actually works, or that it's a sure-fire way to promote your songs instantly. I figured if anyone was serious about their music on this website, they'd like to know about it. I was sure excited when I saw it.
I entered one of my songs, but I'm sure my fanbase is not yet large enough to net enough Amps for me to actually get noticed, but who knows? You miss 100% of the opportunities you don't grab.