As each deal is finalized some of the cargo holds you have assigned to trade may be used to transport the commodities. You can keep track of how many cargo holds you have remaining by looking at the number under the ship on the right side of the screen. When the last cargo hold is used, you will receive no more offer sheets this turn. Each cargo hold can be used only once per turn.
The basic rule for pickup and delivery is that the nation who buys the commodities (the bidder) picks up the commodities in its own ships. Therefore on all deals in which you accept an offer, your Empire's cargo holds will be used up for the turn.
If the buyer is not a Great Power, they have no ships. This means that offers you (and the other Great powers) made that were purchased by tribes or minor nations require Great Power cargo holds for delivery.