Buildings are very important since that is generally how you get domain and they also determine your area of control.

Buildings can normally be built in any space that you can see. When a building is destroyed it leaves a ruin. Ruins don't effect the game unless some card specifies that they do.

Construction Sites

If you play a building in a space you don't control that building isn't created immediately. It first becomes a Construction Site. Construction Sites take 4 rounds without being damaged to become the eventual building. If a construction site is damaged it wont make progress that Round toward completing the building. It will start to finish again next Round.

See in this example if you had built the Ord Stone inside your area of control it would have completed instantly. Instead you placed it outside and now it will take 4 rounds to finish the building.

Construction Sites don't leave ruins when they are destroyed.