Essentially Amazon has — in many cases without publishers' or authors' consent — put a large number of popular titles into a lending library accessible only to Amazon Prime members. Members can borrow one ebook a month for free, and keep it until they download another title — in other words, if they never download another title, they could theoretically keep that ebook indefinitely, without ever having paid for it.
As you can imagine, some people aren't very happy about this, especially since Amazon is doing it without permission. There is an interesting story on the issue on NPR:
Kindle Offers Lending Libraries to Customers
From the story:
Amazon can't include just any book in its lending library. The six major publishing houses have negotiated a way of selling their eBooks to Amazon that precludes using them in a lending library without permission. Smaller houses who sell their eBooks wholesale to the retailer don't have that protection.
Rachel Deahl of Publishers' Weekly says Amazon approached publishing houses last summer with different deals. Most said no, but that didn't stop Amazon from including some of those publishers' titles without telling them.
Pretty scary, that Amazon is so powerful that they feel they can include ebooks in their library without telling the publishers — and, it seems, without offering any sort of compensation.
Here is a blog post on the issues with the Kindle Lending Library from a highly respected blog for writers, including a statement from the Author's Guild with information on what to do if your book is included without your consent.
Yet another example of Amazon throwing their considerable weight around and attempting to use their size to allow them to bully small publishers (and some big publishers too, sounds like). There are good moral reasons why I object to Amazon!