The Access tab is for setting how and when the assignment can be seen and who it can be seen by. Note that if the box for Visibility is not checked, the assignment will need to be linked from another web page.
The assignment can also be connected to a course objective in Access settings. If no group is specified everyone who has access to the event will be able to see the assignment.
Note that if you are not a member of the chosen group, you will only be able to see the page while i the Content editor.