This blue double-ended or 2-way arrow icon means that the folder is part of a shared source you are connected to and thus not part of your own mailbox. A shared source could be a mailbox belonging to someone else, a Public Folder, an Internet Calendar or a SharePoint library.
This overlay icon has been introduced in Outlook 2007 and is also used in Outlook 2010. It’s only a visual aid and doesn’t for instance indicate whether or not the folder is cached. Whether or not a shared folder can be cached depends on the type of shared folder and your version of Outlook.