Sieges are when one nation sieges the city of their enemy they are targeting. They have a couple options for siege equipment, including rams and siege towers. They have a amount of turns to sustain before the city falls. The next log will be about reinforcements.
This is a screen from turn 293, where Benderia has sent the faction heir of their faction, and 3 of his children (in their late 20s) to siege a rebelled city that had revolted due to loyalty. They have at least two legions, and they can build siege equipment.