To be honest I think there is a lot to be desired in the connection between Kindle and Goodreads. There is a lot that you cannot do between the devices. However, one of the best aspects is that you can have your Kindle automatically update a book to your "currently reading" shelf. When you finish reading it will automatically update the book to your "read" shelf and will add your rating. (If you need to connect your Kindle to your Goodreads account then check out this post.)
While I wish that there was a lot more interaction between Goodreads and Kindle this is still a very useful function. The best part is that you do not have to remember to go to Goodreads and remember to add the book that you started (or finished). It is waiting for you in your shelf so that you can add a review. It is also great if you are like me and read multiple books at one time. Since it automatically updates to currently reading I can go back and see what books I need to remember to finish. Am I the only one?
When you first open a Kindle book an about this book screen will pop up. This screen will tell you what book you are reading (although hopefully you already know that), the book description, the average time to read, the books in the series, and information about the author. In addition, there is a Goodreads switch that allows you to switch off the automatic update of marking the book as currently reading. If it is on then when you click off the about the book screen it will automatically update Goodreads. If it is off then they will not talk to each other.
When you reach the end of the book you are given a screen that allows you to update your rating for the book. This rating is updated on both your Amazon account and your Goodreads account. In addition you are given the option to update the shelf on your Goodreads account.
Before you get too excited the available list is extremely limited. It only allows you to move the book to: want to read, currently reading, read, or to remove it from your Goodreads profile. It will not allow it to move it to any custom shelf that you have created. This is a major limitation of the Goodreads and Kindle connection. You still need to log into the webpage or app version of Goodreads to really manage your books.