This refers to a manual, informal method of testing in which an author presents his work and goes through the document step-by-step. The aim is to identify errors, defects, ambiguities and problems.
A walkthrough also has the function of transmitting the document's contents and helping the people present to understand it better. The technique is frequently used by code authors.
White-box testing (a.k.a. clear-box testing, glass-box testing, transparent-box testing and translucent-box testing or structural testing) uses an internal perspective of the system to design test cases based on internal structure.
See also white-box testing on Wikipedia.