When Ouroboros was added to the game, it allowed high level players to return to lower level missions to experience story arcs or badge missions that they might have missed on their way up.
The story goes that there's a time war with bad guys messing up history and good guys (menders) stopping them by making sure events go as they should. This is the essence of the flashback system.
To get flashback missions, you touch a "Pillar of Ice and Flame" which are found in Ouroboros (and can also be put in a superbase as a base item). You will be given a list of all contacts that are below your level range in 5 level increments. When selecting a mission, you will also be given several challenge options.
While doing flashback arcs, you will be Exemped to the maximum level range for that arc and you won't be able to take or enter any other missions (just like being on a task force). Rewards for completing depend on the missions you select, but there are several badges to be had for completing a certain number of flashbacks or completing the challenges (details here).