Normal an exercise is open, that is if an Exercise is visible, students can see the contains of the exercise. The availability of an exercise within the course is normally best controlled through the Visible/Hide activity feature.
The Use Password option is used to associate a "access" password with the exercise. There may be occasions when it is necessary to password protect an exercise. For example, an exercise may be used with several groups of students in a course and each group is set the exercise at different times. The access password is used to prevent the "second" group of students, say, from doing the exercise once the exercise has been opened up for the "first" group.