The mailbox serves multiple functions.
Letters and parcels
The mailbox can be used to send messages to other players, even when they are offline. Sending a message requires paying a $10 fee. Each message can include money, as well as items. There is a 9x3 container space for items in each message. To send a message you have to include a title and a text body, even when sending items.
Items can be safely traded by using the mailbox. Once 2 players agree to a trade, the seller can send the items to the buyer, while using the COD (cash on delivery) option. The buyer will have to pay the price in their mailbox in order to complete the trade.
Currently it's not possible to barter. Items can only be traded for money.