In Rift a Mailbox is used for the sending and receiving of in-game mail. In-game mail can be sent to and received from other players on your shard, and players are able to attach platinum and items to send along with a (typically short) message. The in-game mail system is also used to receive items and platinum from the Auction House.
You can open the mail interface by directly interacting with a mailbox (right-clicking on it when within range). Additionally, a mail icon will display under the minimap when you have unread mail.
Mailboxes are typically located in cities and towns and their location varies wildly. You can track the location of nearby mailboxes using the minimap's tracking function.