Carts are important transportation objects that have a variety of different usages.
Prison Carts - Carts that transport prisoners inside them.
Manufactured Good Carts - Carts that transport manufactured goods from one settlement to the other to your Storehouse.
Raw Material Carts - Carts that transport raw materials from settlements to your Storehouse.
Gold Carts - Carts that transport gold to your Castle.
Medicine Carts - Carts that transport medicine to your marketplace. Note that they function the same way as a goods cart but can be called back to the village at anytime. Also note that they contain 20 medicine instead of 9.
Prison carts only appear in scripted gameplay (e.g. when you capture Crimson Sabatt).
Manufactured good and raw material carts appear when you trade, deliver, or get.
Gold carts appear when you interact with a ruin that yields gold, when you trade, and when allies give you their monthly shipment of gold.
Medicine carts can either appear in scripted events, or can be bought.
To attach soldiers to a cart, select a battalion and right click the cart. Note that when it is an enemy cart, you capture it instead and it automatically goes to your Castle/Storehouse. Also note that you can only guard non-enemy factions' carts, not capture them. Attaching soldiers is a good way to prevent bandits or enemy soldiers from capturing the cart.
Raw material carts automatically enter a storehouse but manufactured good carts stay at the marketplace, wait until the good is all out, and then travel back to your settlement.
- The prison cart somehow has a life as it has a light float above it when it is captured. 
- The delivery person riding the goods cart is the same model as the Harbor Master.
- The Cart driver's whereabouts after transporting a gold/prison/raw material cart is never revealed.
- There is a mini health bar above carts even though they cannot be damaged.