Burning Carts are a great way to take out enemy buildings and to devastate the enemy economy with little to no damage to your own troops. You can also do a lot of damage for example to armoured units, who move slowly and fire will cause them serious damage because of their armour.
Once you left click to attack a building or specified unit, the hay is lit and the burning cart is moved towards the intended destination until it reaches it. Once there, you will have to quickly select another target to attack as well, otherwise the fire will also destroy your own burning cart.
Burning Carts can get destroyed by enemy ranged units incredibly easily, and by enemy melee units as well, so it's important to protect them until the last second when you have already attacked a target, or are about to attack a target. Should your Burning Cart be attacked and destroyed once the hay is alight, then it will leave behind fire in the place it was destroyed, regardless if it does not even reach its target.
Once the fire is left behind it will spread over a period of time and destroy or damage any buildings or units in that specified area. You can recruit a Burning Cart from the rank of Knight Errant. You will need 100 gold for a Burning Cart, along with 1 peasant from the campfire before it can be recruited.
Tip: Burning Carts can be incredibly successful in large groups. If you have multiple Siege Camps located around an enemy estate, recruit several Burning Carts from each and send them all into the enemy estate at once to cause maximum damage. This will likely destroy most buildings in the enemy castle. Burning Carts can also be quite useful in clearing man traps as well.