A unit test typically tests some aspect of a class (in OO languages). There is a school of thought that a unit test tests some behaviour across layers but this isn't correct (that is an integration test).
Good unit tests have a number of features - defined by the FIRST acronym.
Fast
Unit tests should be fast
Independent
It should be possible to run them independently of any dependencies
Repeatable
A test should be repeatable with no manual cleardown or set up
Self-checking
A test should be able to check its own result automatically
Timely
Tests should be written at the same time as the code under test (CUT)
