The Market Box is a place where you can list items for sale, which are able to be purchased by other players. Once you list an item for sale in the Market Box, you can remove it for free and get back your item but you cannot alter the price directly. You begin with four slots for items, but will unlock more as you level up. You can also purchase more slots for Leaf Tickets.
You can view the items a friend has for sale from the Friend List and make any purchases there.