The Department Timed Released function allows content that has been assigned to a specific department to be released to a member after that member has been active on your site for X amount of days.
Articles/Content pages are sorted by "Active Date" within the department they are assigned. Sites like to have articles displayed in departments in an order so the members can follow a plan or read the article in orders. Typically, newer articles (with newer dates) appear at the top of the department page listing and articles with older date will appear at the bottom of the list. Or, if you wanted the articles to appear in alphabetic order, then you would give each the same Active Date.
As a side note, the Active Date function is always set to the day you create the content page (but can be switched) and works together with the "Page Rank" function within each page. Please see this knowledge base article for more information:
The Time Released function will take precedence over your content pages' active dates - only allowing a member to see the content in the department after the specified time period. However, once the member is able to see the articles within the department, they will see the pages depending on how you have set the active dates (even if these dates are far in the past).