The Merchant is a destination similar to Market Town, where you can trade commodities for other commodities. Currently, only some event items can be traded for other commodities. When the event with those items is over, the Merchant destination disappears from the map.
The most recent use of the Merchant was during the 3rd Birthday Event, when you could obtain peanuts from the Peanut Plantation, which you could either trade for regular materials at Market Town or for peanut oil at the Merchant. Both peanuts and peanut oil were stored in the Warehouse.
You can only send items to Merchant if upon return of those items, you do not exceed your warehouse capacity.
For example: Your maximum storage capacity is 5,000, and you have 6,000 items in your warehouses. You want to send 300 peanuts to the Merchant, in exchange for 100 peanut oil. This is impossible, because after the voyage, your warehouse would still be over capacity (6,000 - 300 + 100 = 5,800). However, you could send 3,000 peanuts to the Merchant in exchange for 1,000 peanut oil, because this will take you under your maximum capacity (6,000 - 3,000 + 1,000 = 4,000).