Check out these sources to get an understanding of the role of unit testing in delivering high-quality software:
Read Tim Ottinger & Jeff Langr's
FIRST principles of unit tests (
Fast,
Isolated,
Repeatable,
Self-validating,
Timely) to learn about some common properties of good unit tests.
Read Martin Fowler's
UnitTest to learn about some different opinions as to what constitutes a "unit".