Basically, Google is giving you 5GB of free storage with the ability to buy more storage, to store your files up in Google's cloud. But it seems like unlike with DropBox where you own the files you have on their cloud, with Google, Google can use the files you upload to their cloud.
Here is a video demo of the service:
"When you upload or otherwise submit content to our Services, you give Google (and those we work with) a worldwide license to use, host, store, reproduce, modify, create derivative works (such as those resulting from translations, adaptations or other changes we make so that your content works better with our Services), communicate, publish, publicly perform, publicly display and distribute such content."
This license continues even if you stop using our Services (for example, for a business listing you have added to Google Maps). Some Services may offer you ways to access and remove content that has been provided to that Service.
In any event, it is live and I am sure a lot of people will start using it. I did just to test it.
Update: Here is a statement from Google:
As our Terms of Service make clear, 'what belongs to you stays yours.' You own your files and control their sharing, plain and simple. Our Terms of Service enable us to give you the services you want - so if you decide to share a document with someone, or open it on a different device, you can.