When an Apex class does not achieve the expected code coverage, it suggests that the test methods are not executing parts of the class. The @testvisible annotation can be used to increase code coverage by allowing test methods to access private or protected members of another class. This enables the test method to call methods that may not be directly accessible, but it is not a direct means to generate code coverage. The code coverage is actually achieved when the test methods execute the code within these methods. Therefore, to properly generate code coverage, the developer must ensure that the test methods call the relevant portions of the code that need to be covered. The use of @testvisible can facilitate this process by making otherwise inaccessible code available for testing.
References:
Apex Developer Guide - Testing Best Practices
Apex Developer Guide - @testVisible Annotation