By default, your booking on a calendar gets a visibility from a resource. Customers can book a private resource, but the calendar events will only be visible to you, unless you explicitly mark them public.
Visibility ensures that if you publish a calendar, it will be visible based on your setting.
If you want to make your booking available on a Public calendar, change visibility settings for a booking to Public.
To display booking details like subject and notes on public calendar, choose Public with Subject & Notes option.