It's a common theme in business, including in the indie writing business: Give something away to get noticed, and then (hopefully) cash in on those who like what they see and come back for the non-free products or services. Even for those who don't take the time to get the free whatever, the appearance of the word "free" can be enough to get attention. Increased visibility leads to increased sales. When was the last time you shopped at that one local business that you can't see from the road but can only see their sign? Or, check out your Web-based map service of choice and see how many businesses are near you that you've never heard of because they have no visible storefront or signage.
A typical—maybe even cliché—approach to free books in indie publishing is to make the first book in a series permanently free ("permafree") with the hope that readers who like the first book will pay to continue reading the series. It's not hard to find indie writers sharing their stories of success with this approach.
Another common approach is to use the free-download days that are offered for books enrolled in KDP Select (limited to 5 days per 90 day enrollment). This was very lucrative at first, but changes made by Amazon substantially reduced the effectiveness of this approach. One such change, which had far-reaching impacts, was to give Amazon affiliates ("Associates") a disincentive for promoting free Kindle books.
There are other approaches, of course. Some writers post their work for free on Wattpad. Others make their books available for free download directly from their own site. As I've mentioned here before, I have experimented with distributing free copies of Wolf Block via BitTorrent. Writers selling books directly on Gumroad can use "pay what you want, or nothing" pricing. Free copies can be given away as an incentive to subscribe to a mailing list. Print and/or electronic copies might be given freely, on an individual basis, to bloggers or others with influence. And so on.
This is all done, of course, with the assumption that there will be some value returned from giving books away. The value might be sales of non-free books, or it might be reviews, or something else. It clearly works for some. However, that definitely does not mean it will work for everyone. What little value I can measure from giving away books has been an increase in reviews, but not all of those reviews have been positive.
Part of my lack of success getting value from giving away books comes from having difficulty giving them away to begin with. Despite trying to give away many more, I've distributed less than 10,000 free copies in almost five years since my first book appeared on Amazon. There are writers who can distribute that many free copies in a day or two. So, maybe my writing is just that bad? And, part of it is strategic. For example, Wolf Block—permafree everywhere other than Amazon—is not the first in a series. It is a stand-alone science fiction short story. I had hopes that readers who liked it might then seek out Journey to Yandol, and other stories but, as far as I can tell, that has not happened.
Do you offer a book for free? If so, I invite you to promote it here by linking to it in the comments. I also welcome your thoughts on whether giving books away has worked for you or if it seems to be a dead end.