Apps purchased on the App Store are subject to the Apple iTunes End User License Agreement (EULA) terms and conditions that are agreed to prior to making App Store purchases. The APP STORE AND APP STORE FOR APPLE TV PRODUCT USAGE RULES section of the EULA states the following:
(i) If you are an individual acting in your personal capacity, you may download and sync an App Store Product for personal, noncommercial use on any iOS or tvOS Device you own or control.
(ii) If you are a commercial enterprise or educational institution, you may download and sync an App Store Product for use by either (a) a single individual on one or more iOS or tvOS Devices used by that individual that you own or control or (b) multiple individuals, on a single shared iOS or tvOS Device you own or control. For example, a single employee may use an App Store Product on both the employee's iPhone and iPad, or multiple students may serially use an App Store Product on a single iPad located at a resource center or library. For the sake of clarity, each iOS or tvOS Device used serially or collectively by multiple users requires a separate license.
(iii) You shall be able to store App Store Products from up to five different Accounts at a time on a compatible iOS or tvOS Device.
(iv) You shall be able to manually sync App Store Products from at least one iTunes-authorized device to iOS Devices that have manual sync mode, provided that the App Store Product is associated with an Account on the primary iTunes-authorized device, where the primary iTunes-authorized device is the one that was first synced with the iOS Device or the one that you subsequently designate as primary using the iTunes application.
The rule of thumb
At home: You need to buy one license of an app per iTunes account and can then use that app on all of the iOS devices you own or control and synch with that iTunes account.
Everywhere else: You need to buy one license of an app for each iOS device if that device is used by multiple users or one license of an app per user if that user is using multiple iOS devices.