The department I am in would like to have a kind of "posting" center for questions or a kind of "discussion thread" area only accessible to our department. We would like to utilize Exchange for this purpose.
Because I and the department are not familiar with Exchange, could you advise me as to what is it from Exchange that would best suit us? Is it considered a mailbox?
What you're looking for is called a "Public Folder" in Exchange and it is perfectly suited to your purpose. You can post, read, and respond to messages in them and you can even set permissions to restrict who has access and/or what kind of access they have.
You can create a public folder from your very own workstation (assuming you have the right permissions in Exchange). Click File > New > Folder. Set it to contain mail items and locate it in the Public Folders > All Public Folders collection.
After you've named and created it, the folder will exist on your (and everybody else's) folder list (View > Folder List) under the Public Folders > All Public Folders section. Right-click the folder to access the Permissions tab where you can grant, modify, or remove permissions for any users in your organization.