Black-box testing uses the specification of a component's external behavior as its only input. It is mandatory to determine if the software does what it is supposed to do and doesn't do what it is not supposed to do. White-box testing uses the code itself to generate test cases. Thus white-box testing might demand, for example, that a certain level of code coverage is obtained. Be aware; however, that even with both black-box and white-box testing, testing can make use of only a small subset of possible data values from the input domain.
To demonstrate how black-box and white-box testing complement each other, let's look at an example. Let's say a procedure's specification states that it should print the sum of all numbers in an input list. When programmed, it looks for one input of 213 and, if it finds it, sets the sum equal to zero. Since that was not in the specification, there is no way to find the error by black-box testing except by accident. White-box testing would demand that paths are more adequately tested, and thus would probably detect the "213" situation. By combining black-box and white-box, you maximize the effectiveness of testing. Neither one by itself does a through test.
Reference:
Dunn, R.,
Software Defect Removal, New York: McGraw-Hill, 1984.