All I can find in the manual is how to turn it on, but not why or what it does.
With the latest firmware, Chapter mode has a dual function.
Originally, with .aa format Audible books, Chapter Mode allows you to navigate between the chapters of the loaded book. The chapter number will also display on the screen.
With all other audio books, Chapter Mode allows you to skip between files labelled for the same book. In normal mode, the skip feature is disabled. You can rewind or fast forward within the book file. In Chapter mode, a single press moves to the next file, just like with music.