white-box test design technique

ISTQB Glossary  definition 

"Procedure to derive and/or select test cases based on an analysis of the internal structure of a component or system."

In simple English:

In essence, you as a tester will know the internal working of what you are testing. 

Your test design and execution will be based on your knowledge and understanding of the code being tested. 

Field Notes 

1. It's very easy to understand this, if you read it as transparent box testing. 

2. The tester in this case will have to be comfortable with technology used to build the system being tested. 

3. More than comfort, tester being competent in the technology is essential. 

4. Usually mission critical systems and systems that have a huge impact in terms of money involved our time is tested this way. 

5. Products that are built to be the foundation for lot more things in the future are tested like this. 

For Example:
Say, you want to test the software that controls an rocket. What you need to be sure of its that there is no piece of code that might bring the rocket down.