What is black box testing and White box testing?

Black box testing is also termed as functional testing. It ignores how the internal functionality of a system works and depends only what are the outputs on specified inputs. Source code availability is not an important in back box testing. Black box testing is mostly to ensure that it meets the user functionality.
According to IEEE standards following are characteristics of Black box testing:-
Testing that ignores the internal mechanism of a system or component and focuses solely on the outputs generated in response to selected inputs and execution conditions;
Testing conducted to evaluate the compliance of a system or component with specified functional requirements.
One of the ways of black box testing is Manual testing what the tester performs. For instance you can install the application on a machine and tester starts testing is a type of black box testing. In this case the tester is completely unaware of the how the program logic flows and how its coded etc.
White box testing is opposite to Black box it requires internal know how of how the logic flows. As this testing needs know how of the internal structure it can only be done programmers. Unit testing is one of the ways of doing White box testing in which programmers use NUNIT or JNUIT to test each class individually. White box testing can be done by programmer by either stepping through the code or testing the classes and components in isolation.