Empyrean Age will add combat zones, militia missions, and combat sites (which are distinct from combat zones). The term "combat zones" refers to the two stretches of contested space lodged inbetween the Caldari and Gallente, and Minmatar and Amarr civilizations. Militia missions are like regular missions, but they'll send you into enemy space, where you'll have to do battle with hostile players.
Combat sites are exploration points which will show up on your sensors as cosmic anomalies. These are territorial capture points. If you capture enough of them, your faction will be able to attack the system's control bunker. If the attack is successful, then the system will change hands during the next downtime.