I would say that a unit in unit testing is a single piece of responsibility for a class.
Of course this opinion comes from the way we work:
In my team we use the term unit tests for tests where we test the responsibilities of a single class. We use mock objects to cover for all other objects so that the classes responsibilities are truly isolated and not affected if other objects would have errors in them.
We use the term integration tests for tests where we test how two or more classes are functioning together, so that we see that the actual functionality is there.
Finally we help our customers to write acceptance tests, which operate on the application as a whole as to see what actually happens when a "user" is working with the application.
This is what makes me think it is a good description.
