Because Andy set completion tracking on his course, that course becomes available as a prerequisite for Stuart when he clicks on the Completion tracking link.
Stuart chose this as a prerequisite for his course. Students like Emma won't be able to have their French course marked "complete" until they have shown that they have finished Andy's course:
Additionally, Stuart doesn't want his students to use the self-completion option for his course. Instead, he wants them to have tackled three assignments, so he checked these in the Activities completed section:
When Stuart looks at the Course completion status block at the start of the course, this is what he sees:
Emma finished the How to Be Happy course by marking it complete herself so that prerequisite is checked. Once she has done the other necessary tasks they will be checked too and Stuart's view will change accordingly: