When completion tracking is enabled, course content and assessments can be assigned completion conditions.

This is useful for ensuring students complete requisite materials. 

• You can make the completion of one activity - for example, a course reading - a requirement in order to access a quiz.
• Or you can make passing a quiz a requirement to view the next course section
• etc.

Individual completion settings are set within each individual activity component.

When Show activity completion conditions is also set to Yes, students can see the course content and assignments they have completed as well as content and assignments that are incomplete, directly on the course homepage. 

e.g. 

You can have completion tracking enabled, but set Show activity completion conditions to No.

This allows you to apply completion conditions to various course components without these conditions appearing on the course homepage for students.
The conditions will still show for students when they open the Activity itself.

Under your course admin is a Course Completion menu:

From this window, you can set completion settings and requirements for ALL ACTIVITIES in your course - or even to just apply to some activities and not others.

For example, to turn off activity completion on all elements. Select Bulk edit activity completion from the dropdown menu.