Subjugation is the Cuotl equivalent to buying cities and other sites. It uses timonium, since cuotl don't have wealth, but costs more, since timonium is easier to get than wealth. Once used, the target building and defending units lose a large portion of their health and become the player's units. Only the Cuotl can use subjugation, but repairing a damaged building can be a hassle!
The Judgement line of research reduces subjugation cost and building and unit damage, meaning that repairing the building is cheaper and so is subjugating!