Cancel on the Audible website, not in the app: select your name, View membership details, Cancel membership, then confirm. Use your credits first, because unused credits are lost.
Steps
On a computer
Sign in on the Audible website and select your name at the top.
Select View membership details.
Select Cancel membership.
Select Continue to cancel.
On a phone browser
Open the Audible website, tap the menu and tap your name.
Tap View membership details, then Cancel membership.
Scroll down and tap Continue cancelling, then Cancel anyway.
Choose a reason and tap Submit.
Billed by Apple or Google?
If you subscribed inside an iPhone or Android app, the app store bills you and you cancel there.
Billed by Apple (iPhone or iPad)
Open Settings and tap your name.
Tap Subscriptions, then the subscription.
Tap Cancel Subscription.
Billed by Google Play (Android)
Open play.google.com/store/account/subscriptions on your phone.
Select the subscription.
Tap Cancel subscription and follow the steps.
When it ends
Your membership, credits and Plus Catalogue access end after your final billing cycle.
Good to know
Deleting the app does not cancel your membership.
Unused credits are lost when the membership ends. If you want to keep them, you may be able to pause instead.
Books you bought with credits or money stay in your library.
Joined through the App Store or Google Play? Cancel there instead (steps above). Credits from those memberships do not expire.