Task Lists are best described as simple, flat categories for tasks. You can define as many lists as you like and optionally assign them to milestones. Basic and self-explanatory form fields such as Title and Description are not covered here.
Project
When creating a new list, you must select a parent project. Once you save the list, the selected project can longer be changed. The project will unlock and govern the available milestones and access groups you can select in this form. So its a good idea to select a project first, before continuing through the rest of the form.
Milestone
You can optionally assign the list to a milestone. If you do, the milestone may influence which user groups for permissions are available.
Status
Changing the status of an existing list will also change the publishing status of all tasks that are assigned to it. For example, archiving the list will also archive all assigned tasks underneath it.
Permissions
In order to see and change the permissions, you have to be an administrator. Non-Admins will not be able to set the task permissions. Instead, the access of the selected parent item (milestone or project) will be inherited. If you are an admin, the groups that are available for selection is limited by the access of the selected parent item - again, milestone or the project. For example, if your selected project has selected the "Registered" group, you will not be able to select the "Public" group here, because it lies outside the containment.