What does the blue arrow icon pointing left and right on a folder mean?
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.
Blue arrows on folders icons in a shared mailbox.
Note that the blue arrow icon isn’t shown on default mail folders which already hold an overlay icon of their own such as the Inbox, Sent Items and Junk E-mail folder.
For an overview of the meaning of all folder and item icons see; What do the icons mean?