Total War: WARHAMMER Wiki
See siege battle for the battle side of things.

On the campaign map, a siege involves one army attacking an enemy settlement which has walls and a defending army (usually including a garrison army if nothing else). The attacker can surround/encircle the enemy settlement, construct siege weapons which takes a certain number of turns, break the siege or continue the siege. Each settlement has a hold out time - a number of turns which will count down while they are under siege. If they are still under siege when this hold out time runs out, the defending armies/garrison will take siege attrition.

The following are halted while you under siege:

A defending army can choose to sally out and attack the attacker, which results in a field battle. If the attacker attacks, then it will be a siege battle.