Within every empire, there exist those who train mercenaries, build instruments of war, and stockpile food. If your empire's Blacksmiths and Farms do not produce enough to sustain its citizens and army, you may spend your money here to purchase these goods.
Only a finite number of goods can be purchased from the private market in a given time span - once depleted, you will need to wait for more to be produced. The rate at which units and food are replenished is based on both the overall size of your empire and how many Keeps and Farms you have, respectively.
The cost of goods on the private market is affected by your economy and your ability to maintain such units - having a large percentage of your empire occupied by Markets and Keeps will reduce the purchase prices of military units by up to 40%; however, food prices are not affected.