We don't use the Kindle too much, but pretty soon it gets reall cluttered. There are book loans from our library that don't get cleared for isntance. YOu have to manually whack each one in the web app or just hide them from the Kindle app itself:
If you are talking about the Carousel, which is the first shelf, you can do a tap hold on the upper right and a selection box will pop up and you can remove it from the Carousel.
If you are talking about the lower shelves, called your Favorites, these also can be removed in the same fashion. They will, however, remain in your books or apps as well as the cloud.
If you want to delete them from the Cloud, then you need to go to your Manage Your Kindle page and after deleting, then return to your Kindle and do a sync to have it correspond to the MYK page.
Once deleted fro the Cloud, you will no longer have them and will have to purchase them again if you want them back. Amazon.com: Customer Discussions: Can I hide books on my Kindle Fire?