A few definitions of unit tests from various sources ...
A unit test is an automated exercise of code.
A unit test is written for each module (class), in isolation, to verify its behavior.
Unit tests are tests that you, the developer, create to exercise your code and prove that it works, i.e., prove that each of your methods meet the criteria of its contract.
Unit testing is a form of ``white box'' testing.
In combination, unit tests can be used to create large regression tests.
C3 (the famous Chrysler C3 project) has over 1300 unit tests, performing over 13,000 individual checks. They run in about 10 minutes.
