The primary objective of any campaign is to win PvP matches, be they single instances or many using the Base Raid mechanic. This gives the Alliance that specific territory, and whatever bonuses it may grant. Once the territory is captured, a number of improvements can be built.
Also, once a territory has been won, it may be possible to retake from the existing owners; however this mechanic is suspected yet not confirmed.
Each campaign lasts 45 days and at the end of this, presumably the Alliance with the most number of territories will "win" the campaign and will have dominated the world. It is not yet clear what bonuses (if any) this will grant. The leading agency will then have to retake the objective's on the map from the start.