‘Areas of Responsibility’ is a way to separate the different areas of your life. Some examples might include: Work, Home, and Hobby. When in an Area, you will only see the tasks and projects that pertain to that Area. This is a good way to separate different Areas of your life so that you can concentrate on just one at a time.
To access an Area, simply click on the “All Areas” rectangle on the top left corner of the screen and choose an Area to view.
You can create new Areas in Manage Areas... After creating new areas you can then assign Projects to a particular Area. This will help you organize your tasks even further.
June 2017 UPDATE: Based on popular vote and a lot of passionate discussions among our team, we've added "No Area" to the Area filter list. So now you have a way to view all tasks and projects that are free roaming or don't belong to an Area.
See also: How to edit an Area