It runs Android, but a full customised Android that you don't have Google Market, Gmail, and the Android update … It officially only supports Amazon's services.
In other word, it's a branch out from Android master. And it will never merge back.
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Amazon's Kindle Fire tablet: Some important perspective
I went to a presentation by Amazon the other day, and they discussed this. They state that really their device is simply a skin, and no real changes have been made to Android itself (distinguishing between the apps and the OS). It is true that they've stripped off the Google goodness, but in theory you could just add it straight back on via side loading (assuming that is allowed)
They were a bit cagey when pressed for how often it would be kept up to date with new OS releases. The best they would say is "We're a tech company. We'd like to think we'd be better at providing OS updates than the Telcos". Reassuring? Perhaps not.
Amazon definitely plan for this to be an Amazon device, not a Google device with Google add ons. I think its a very smart move on Amazon's part. I reckon that competition is a good thing.