Siege is a strategy for attacking a castle. One example is when an army can camp around a castle and wait for the people inside to run out of food. The people are forced out of the castle because they have nothing to eat and that's when they get attacked. Another example is using weapons.
Armies can attack using catapults with dead animals. Catapults would throw dead animals over the walls to make them sick. They liked the siege because they might get the lord to surrender. Sometimes it could take months or years to work.