If, as the leader of an ambitious young House, you see a city that you think would look good with your banners fluttering above it, starting a Territory War is how to begin the process of adding it to your portfolio.
Since the current development plan is to rank Houses according to their fiefdoms, securing resource hubs (mines, farms etc) and settlements will be key to establishing their economic status and military power, while holding a city is a prerequisite for founding an alliance. Leaders pick their targets by scouring the world map and right-clicking on strategic targets to “declare war” on their current occupants.
By using a Wax Seal from their inventory, war declarations are made official and the shameless aggressor must them select a one-hour time slot within which the target has to be taken by force. If the attacker fails to turn up, or the battle goes badly, the city will remain in the hands of its current owner. Fare the day well and the new lords of the manor can start imposing itself upon the local populace.
While time slots do give defenders an advance warning to prepare (defenders can make a pre-emptive strike on attackers moving across the map), the system is a necessary one in a game that spans multiple time zones, as it allows both sides to assemble their forces and assign tactics. Given that not that many medieval battles were surprise attacks anyway, the time slot system isn’t completely removed from how sieges and pitched battles were often undertaken.
During Territory War battles, victory for each side is assured when the enemy's base camp has been captured. If at the end of a losing battle for the defenders the time slot is not yet over, a counter-attack can be mounted, but if time is up (individual Territory War battles can last up to 30 minutes), ownership changes and the victor can start developing their new holding - and enjoy its growing status as a major regional superpower.