Amazon seems to be in the process of opening up a new feature: Kindle Unlimited, all the Kindle Prime books you want for $9.99 a month (US only of course). The Prime borrowing catalog is about 600k books right now.
(ETA: The new Kindle Prime feature also includes the Audible Audiobook catalog, which may be a killer feature for borrowers).
This is clearly a shot at Scribd and Oyster, which have similar schemes, and fairly big catalogs. It might be interesting to look at, but I am not so sure it's going to be a big hit.
Firstly, you should understand how Prime borrowing works. Anyone can publish a book via Kindle Direct Publishing (KDP), but authors can also sign up to be part of a program called KDP Select. Books in Select have some rules: They can not be made available for sale elsewhere while in the program being the main relevant one here. They also have some benefits, such as the ability to hold countdowns to sale days with reduced prices, and being part of the Prime lending pool.
In the Prime lending pool, any Amazon Prime member currently gets one free borrow, any book in the catalog, per month. Amazon puts up a pool of money, which varies a little per month but is lately around $2 million, and it is split between the authors pro rata. If a million books were borrowed total during the month, and 3 of them were yours, you would get 2 million/1 million * 3 = $6. This is a flat amount and irrespective of the normal royalty rates Amazon pays so the borrow money could potentially be higher than your royalty for selling a copy. A few authors make substantial money out of this, market the borrowing heavily and it is their main incentive to stay in the Select program. Most authors get one or two borrows a year if they're lucky, so it's not currently an incentive at all.
Meanwhile, Scribd and Oyster, which offer a similar service, pay the full purchase royalty (ie, you earn exactly as much as if you'd sold the book) for a borrow on their services, and both have good trad pub support, although both are mice compared to Amazon's Elephant.
So, how's this break down:
For readers: $9.99 for all you can eat and read on your kindle, is a great deal. What I wrote above about KDP Select doesn't apply to trad publishers, so there's quite a lot of non-indie books in that 600k catalog, although it's hit and miss what is in there. While borrows are one a month, as a side-feature to the big Prime feature of free shipping, it's really easy to forget to even use it, but when you're paying a monthly fee, I suspect it'll be less easy to forget.
For non-Amazon readers: Some of the indies are going to be tempted to put their books back into Select, which will mean taking them out of the other sales channels - Obviously Amazon would love that. On the other hand, any author making substantial money on Google Play (and there are plenty now) or Kobo is going to be pretty loathe to put the book back into exclusive to Amazon land. Select is a 3 month sign up,so we might be seeing books bouncing in and out of availabilty on other stores, which would be mad annoying.
For authors: A big choice to make. Gamble on the borrows outweighing the potential income from other sales channels, or not. There's also the question, since Amazon haven't said if the borrow pool money will be increased. $2 mill or so at current borrow rates, some authors are making a killing. $2 mill at 10x or 100x the number of borrows? Not so much. As soon as it goes under the royalty rate, authors will be screaming and pulling their books out as soon as their 3 months are up, so I suspect it will be increased, but I also suspect it'll never match what you could make on Scribd.
Anyway, it's all very interesting watching the industry manoeuvering around Amazon, and Amazon manoeuvering right back. And if you happen to have Prime membership anyway, watch out for notice of this new feature.