Audiobooks are available from Apple through the Books app. Apple doesn't offer a subscription service similar to that from Audible, but often has attractive offer prices on selected books. Books may be discovered, purchased and played using the Books app.
The Books app has 5 tabs at the bottom of the screen on iPhone. On iPad, these appear as a sidebar. If the sidebar is hidden on your iPad, tap the show sidebar button near top left of the screen.
The "show sidebar" button
The iPhone tabs or iPad sidebar options are "reeding now", "library", "bookstore", "audiobooks" and "search".
"Library" shows the books you have purchased. "Bookstore" displays featured print books and offers. "Audiobooks" displays featured audiobooks and offers and "Search" allows you to search Apple's store of print and audio books.
The search initially searches simultaneously for print and audio books.
Three buttons will normally appear above the search results labelled "All", "Books" and "Audiobooks". You can use the Audiobooks button to restrict your search to audiobooks.
Purchasing and listening to audiobooks through the Books app should be fairly easy from this point.