Double Agent PvE missions are similar to standard PvE missions, but with a twist: instead of 4 players in the mission, there are 6 - and 2 of them are randomly selected to fight on the NPCs' team. The goal of these two "double agent" players is to thwart the efforts of the other 4. The 4 players who are not double agents have the same goal as in a standard PvE mission; kill the final boss of the mission.
Double Agent missions require a minimum level of 25.
Note that the more often you decline PvE mission queues, the less likely you are to be selected as a double agent in this queue. (Thus, trying to "game the system" by declining/leaving missions in which you are not the double agent is counterproductive.)