Ok, everything you are reading right now stems from an article written by Billboard, which you can read
here.
I should also note that while Billboard has impeccable inside sources for the music industry, this is leaking during ongoing negotiations, so this could change. There are two main parts to Google Music, and I think they'll be well worthwhile:
1) A music store much like iTunes, but accessed through a browser (and/or a mobile app on your phone). They hope to let you preview an entire song once before you have to buy it. You will be able to buy (and download) and own the song for a price competative with iTunes. You may also be able to do a Zune-like subscriptions service, that hasn't been detailed.
2) There will be a cloud-based "storage locker". For $25 a year (not month!) Google hopes to make available to any browser (or mobile device) that you sign in to the music you buy, plus any music you own on your computer. That would be all DRM-free music + any DRMed music that the industry agrees to (word is iTunes DRM is supposed to be included). So that would be the "syncing" part of it, where all of your music is available from the cloud on your phone, and of your computers, or any other device with a browser.
Presumably there will be a limit to how many people can be logged into your account simultaneously (I'd guess 2 or 3) to prevent you from pooling your accounts with that of many other friends, relatives, etc. You will also have the option of downloading your music onto your phone or computer so you have local copies if you want, but if you own tons of music you won't have to store it all if you don't want to.
If they manage to get this list of things in, I know I can pledge many years of dropping $25 a year. It will also neatly remove the tether for millions of people to iTunes in one fell swoop. Of course Apple is trying to get a cloud-based service to market as well, and people will have different preferences. But like I said, if they pull this off as leaked they can count me as a customer.