Story Arcs are special setups in the game that reveal a piece of the story content over a series of missions from a Contact. The number of missions can be small or large, but will all function as miniature stories themselves. Upon completion, a Souvenir is rewarded which allows you to read the storyline at a later time. This summary is saved in a user's clues menu. Completing a Story Arc will net the player a significant XP bonus and, for most arcs, the choice of one of many types of Enhancements.
There are actually two types of Story Arc. Main arcs are signified by a yellow-covered book icon in the arc contact's window. Shorter, minor arcs are signified by a red-covered book. Each character may have a maximum of two active Main Arcs. Contacts will not give missions that start a main arc if you are at the limit. While there may be a limit to minor arcs, there is no functional limit as there are reports of characters with as many as 23 minor arcs open at once (source). Note that for Heroes, the zone-specific arcs from contacts in The Hollows, Faultline, Striga Isle, and Croatoa are all minor arcs and for both Heroes and Villains the missions in Rikti War Zone are also minor arcs.