A siege is when you are attacking a castle. Also trying to surround and take the resources of the castle. A siege can also happen in a town or building. Sieges happened because they wanted the people they were attacking to have less resources.
One example of a siege weapon is the ballista which is an old weapon used to throw large bolts. Also the ballista was better than a catapult range wise. The ballista was a similar model to the crossbow.
In addition they used a ballista during battle and during a siege. The ballista was used to throw large rocks and hit the people, also it was used to take down walls.
When using a ballista you have to be close to get the force that you want. This is because the range is short.