Here's what I know so far (based on sending stuff to my Kindle this morning, reading the help pages, and looking at the Manage Your Kindle page).
Everything that you email to your Kindle (any of your Kindles) will be archived by Amazon. They're giving you 5GB of free storage just for your Kindle files. Note that the 5GB is completely separate from whatever amount of space you have in the Amazon Cloud Drive; I actually have 20GB in the Cloud Drive but only 5GB for the Kindle files.
I've tested the service, and files sent to my K3 and my K4 (not yet arrived) have been archived by Amazon.
There's a new set of menu options on the Manage Your Kindle page, and it looks like I cannot do everything with my files that I could already do with stuff I bought from Amazon. I cannot download the personal files but I can send them to my new K4 or the Kindle Touch (which hasn't even shipped yet).
Note: This new feature is only fully supported on the new Kindles, just like I surmised on Sunday. I can also confirm that the Amazon help pages say that Amazon will archive your annotations. Again, I suspect it will only work on the new Kindles, but this is not clear.
I don't know about you but I've been wanting something like this ever since the Kindle launched. I would have been willing to rent a GB or 2GB of space in order to get this service, and once I had a Dropbox account I would have been more than happy to give Amazon access to it.
But I also have to question how Amazon went about implementing this service. They gave me 5GB for my Kindle but won't let me use the 20GB I already have in the Amazon CD? That's a tad schizoid, and in the long run they will likely have to combine all their cloud storage services into one system.