As part of the redesign of the music app in iOS 8.4, Apple has outsourced the audiobook function. This is now including a new look in the iBooks app.
As 9to5Mac stated, audiobooks in iOS 8.4 are no longer a part of the music app, but iBooks app. The app brings further with a new surface, which provides, inter alia, improved support of finger gestures.
The new player is similar to the new music app, but offers some adjustments that are especially useful for audio books. Thus it can be quickly rinsed by 15 seconds forward or backward by a wiper to the left or right on the cover artwork. By keeping the gesture you can adjust the speed, maximum one may take a minute move back or forward. A small icon in the upper right is a shortcut to the chapter.
To the owner of a car radio with CarPlay Apple has also thought. To access the audio books there is now a separate app on the home screen.