If you mean Kindle Fire EBook reader, then it is meant for reading EBooks and not much than that.
On the other hand if you mean Kindle Fire tablet, it is almost similar to an Android tablet.
The major differences can be elaborated as follows -
1. The first difference that comes to your notice is the interface. On an Android tab, the appearance will look something like what you see on your desktop. All the items will remain as you placed them until you move them. On Kindle fire , the home screen is called a carousel. It will give focus on recently read EBooks, Amazon Music and apps. Amazon has more control on what you are seeing on the Kindle.
2. You can have access to your apps on Google Play Store. But while on the Kindle Fire tablet, you have to depend on Amazon app store. It will mean you will be forced to wait a little more for the apps to arrive on Amazon Play Store. But it will ensure improved quality control of the apps.
3. Silk browser is the only browser you can use on Kindle Fire tablet. On the other hand, you have access to Chrome, Firefox and a host of such other browsers for an Android tablet.
4. EBooks that you can read on Kindle Fire need to be from Amazon. You will not have access to any other EBooks. While on an Android tablet, you can install respective apps for different EBook providers and get the EBooks on your tablet.