Structures are the infrastructure of your realm.
The lifeblood of your empire, Cities constitute colonies and urban centres which expand your Borders and allow for the construction of Economic structures in new territory.
Economic structures are just that — their primary task is to drag resources you can use to either create more buildings, or create minions from them to impose your will and ultimately win the game.
The task of Recruitment structures is a very crucial one, for they are the buildings in which units are created, housed, fed and maintained — without them, your nation is completely defenceless.
What more can we say?
The main task of Defensive structures is to function as point defences to help defend your settlements (not to mention, attack and kill intruders).
While not directly involved in defensive or production duty, enhancements are vital infrastructure which allow access to upgrades which improve your faction's power — be it economic, military, or otherwise.
Wonders are special buildings which if built in sufficient numbers, can generate wonder points that count towards a victory condition. Wonders function like enhancements, and can sometimes be used to train troops. A few wonders are also powerful enough to function as defensive structures.