As per Wikipedia, Business Process Validation (BPV) is the act of verifying that a set of end-to-end business processes function as intended.
In other words, this is not checking that the app doesn't crash, rather, it's checking the app does what you designed it to do.
So, in your example of writing a use case for creating a user, the Business Validation would include the ability to retrieve the user - and all the information they included when signing up.
It could also tests to ensure that the user is uniquely identified in the system; that there's no way the system will confuse users with identical names, for example.
For that matter - depending on the spec - it may refuse to create new users with identical "identification".
It could also include checks to ensure their payment method is valid, their password is of correct length & strength and that - if implemented - they have confirmed their email by clicking in the email they received by the system.
In the latter case, it would define what the user can/cannot do until they have confirmed their email - and this too has to be checked that it is implemented as expected.