Sacred Spaces provide players with the opportunity for special bonuses for defeating barbarians!  In order to attack a Sacred Space, players must first send their legion there (to send Legions onto the map requires all barbarians in your suburb to be cleared).  Sacred Spaces can only be accessed by legions from within the same Province, but anyone can enter a Sacred Space, regardless if their city owns the Sacred Space or not.  
When you enter a Sacred Space, you will be randomly placed in one of 16 different lanes.  You will be locked to this lane until all of the barbarian huts in it are defeated.  In the middle of and at the end of each lane is a "treasure camp" that will provide special rewards for being defeated.  Once a lane has been finished, you will not be able to re-enter the Sacred Space for a period of time declared on the UI panel of the Space.