These are areas in which players playing on a PvP server will find their PvP flags turned on. Any player can be attacked by a player of an opposing faction while in these zones. Some contested territories are Alliance favored (generally they will have more Alliance outposts, cities, or are just closer to a main Alliance city or territory), some are Horde favored, and some do not favor one faction.
Generally, once a player on a PvP server hits level 20, he or she will have to start questing in contested territories. Pretty much at level 30, all questing must be done in contested territories.
There may be neutral cities within these zones where Alliance and Horde can coexist.