Traders have a greater reach to see offers and can broker deals ie. connect Buy and Sell Orders. They can also broker multiple deals as long as the orders match up. So Ii region A has a sell order for 200 Food for 20 gold/100 Bushels, region B has a sell order for 300 food for 15 gold/100 Bushels and region C has a buy order for 500 Food for 25 gold/100 Bushels, the Trader can broker these deals to buy 200 food from region A, 300 Food from region B and sell that 500 food to region C. The profit for the Trader is the difference in price. Cost to buy food: 85. Income selling food: 125. Profit for the Trader's pockets: 40 gold.
Non-traders have a smaller reach and can only accept a sell order or accept a buy order, not match them up. Though you can easily simulate the matching by accepting the buy offers first, then accepting the sell offers. I guess that's not a real advantage of the Trader. The greater reach means he can see more deals then others though, allowing him to be better at this matching up offers.
