A sample run is a simulation of a user session from beginning to end.
It is also called a "story".
For example, suppose the software system is for test generation
and testing. An instructor first logs in, then selects the option
to create a test ABC for course 123.  For this test ABC, the instructor
decides to have 10 problems.  The first problem is a new multiple
choice problem, the instructor enters it.  For the second problem,
the instructor decides to reuse an existing problem. So the
instructor must search the test database to find course 123, then test XYZ,
choose problem 3, modify it a little, and make it the second problem.
The instructor proceeds similarly, until all ten problems are created,
and stores the test ABC in the test database.

The user manual not only contains detailed explanation
of each step.  It should also have a sample run as described above.
For many users the best way to learn a new system is to follow
a sample run.  People usually don't want to read the entire user
manual.  That being said, you still need to add more explanation
to the user manual so that it becomes easier to follow.