Moodle 2 offers a host of new functionality when compared with version 1.9. One of the options that users have been demanding for a long time is the possibility to make course resources and activities interdependent. That is, course activities become accessible to students only under certain conditions, for example, that they have completed another activity and/or obtained a certain grade for it.
In Moodle 1.9 only the Lesson module had this functionality (i.e. access to a lesson could be made dependent on success in another lesson. Moodle 2 has extended this functionality to all activities and resources in a course. If you want students to read a document before they attempt an assignment, you can make the assignment access dependent on the students having viewed the document. If you have a series of related quizzes in a course, you can stop students from accessing quiz 2, before they have completed quiz 1. And so on.
In the above completion is already mentioned as one of the conditions upon which you can make access to course activities or resources depend. Activity completion is related to the Restrict access function, but can be used independently. The advantage of using activity completion is that students can track their course completion, in a block called Course completion status, i.e. they can see if they have done all the tasks required of them in the course.
Does this all look and sound too difficult? No worries, you can then ignore the Restrict access and Activity completion settings whenever you add an activity or resource and it will work normally as in Moodle 1.9.