white-box testing

ISTQB Glossary  definition 

"Testing based on an analysis of the internal structure of the component or system."

In Simple English,
it is testing done with complete information and knowledge of how the internals of the component or system under test works available and used by the tester.

Field Notes 

1. This is also called Glass box testing. Glass box because the tester can see what is inside.
2. Often people assume it as knowing the code and testing. It is not often the case. 
3. Testing the code directly is part of unit testing and not strictly a functional test in the broad sense of software projects.
4. This is still a functional test.
5. This testing needs the tester to be proficient  with the internal structure of the system under test.
6. Getting help from a developer does not count as a white box testing as more often the lack of knowledge and understanding undermines the test objective.
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For Example: