Pushing the button means you will have a copy of those songs until sometime in 2019.
When I log in to view my subscription, I get this notice:
"Your music storage subscription which enables you to import up 250,000 songs will expire on April 8, 2018
After this date you will not be able to renew your subscription or upload more songs. In order to continue to play and download your uploaded songs after your subscription expires, select "Keep my songs." Otherwise, these songs will removed from your library. Amazon music digital purchases will remain securely stored for playback and download."I'll probably end up reviving a Plex server and setting that up, it was just nice to be able to mix streaming services with owned music in a transparent manner.
Edit: ok I found the difference on this page: https://www.amazon.com/gp/help/customer/display.html?ref_=dm... Basically if you don't push the button, they will delete your files. If you had a paid storage plan, they will keep your original files somewhere, but they won't be accessible from your music library. If you push the button, you can continue to play and download your music like normal, but you still can't upload any more.
Amazon is dropping that backup.