Each epic mission arc is a special series of missions tied together in a dramatic story. These are often more difficult than standard missions of "equivalent" level, but have better narrative and often better rewards. The last mission in each arc gives a significant faction standing boost - with no derived standings changes to other factions - and may also award a valuable item. Each epic arc has at least one branch point where your decision of how to continue will affect both the story and your rewards.
The epic arcs can involve a lot of travel, but many of the missions can be accepted and/or completed remotely to reduce travel time. Epic arc missions do not expire, and each arc can be repeated every three months.