Serial publication (in which books are published chapter-by-chapter) has a long history in the world of fiction, and in the future, we believe serial or "in-progress" publishing will become the norm not only for fiction but also for non-fiction.
Twenty-first century publishing technologies, specifically related to ebook publication, allow authors to update their books with new chapters and errata fixes easily and instantly.
They also allow authors to interact with their audiences in new ways, which can shape their books as they are published in-progress.
By purchasing and reading a book before it's finished, you can be part of the process of the book's development, and crucially for some non-fiction books, you can read an author's latest work without having to wait through the arbitrary delays caused by the constraints of earlier forms of publishing.
For more information, please see this talk by Leanpub co-founder Peter Armstrong: