Bishul, cooking, occurs when one heats up a liquid past yad soledet bo in a utensil. Bishul uses indirect heat, meaning that the food is not being heated directly from a fire, rather the heat is being conducted through a pot before reaching the food. Bishul can occur with just a liquid, or a liquid with solids in it. When bishul takes place, there is an equal transfer of taste between all ingredients in the pot. The bishul also transfers taste from the food to the pot and back.
If a pot had forbidden food cooked in it, and then one cooked permitted food in it, the bishul would transfer taste of the forbidden food to the pot in the first cooking, and subsequently to the permitted food cooked in that pot later on. The same would be true if one cooked meat in a pot and later cooked milk, the meat would impart taste to the pot and then when the milk was cooked in the pot the taste of meat would get transferred to the milk and the taste of milk would go back in to the pot, forbidding both the milk and the pot.