Thank you Brian for your question. You are going to LOVE Audible.com. I have been listening to audio books from them for years and it is even better now I can listen to my favorites on my Kindle too!
To answer your question though... When you purchase an audio book from audible.com, it is very similar to purchasing a book for your Kindle. You can listen to it on your Kindle (with or without earbuds), or any one of a number of other players (including your iPhone or android phone) and when you are finished with it, you can remove it from your device, but it will always be available in your library, much like the archives on Amazon.com. You purchase it, it is always yours as long as you have that user id and password. And now Audible.com will let you use the same user id and password you use for your Amazon.com account, so it all should be pretty seamless. With your Kindle, if you browse through the archives, you should see any audible.com audio books listed with the word audio or audible (I can't remember and don't have my Kindle handy at the moment) next to the title.
Special Note: In order to download audible files directly to your Kindle, it must be on a wifi connection. 3G won't get it. If you can't get wifi on your Kindle, you can still listen to audio books but you need to download them onto your computer and transfer them to the audible folder on your Kindle by hand using the USB connection to your computer.