A Faction Event is a unique scenario, typically lasting for about 5 days, in which a particular Faction or several competing Factions call on Starfleet to aid them in a variety of related Shuttle Missions.
These Shuttle Missions function in much the same way as regular ones, with a few exceptions. Event Shuttle Missions will operate as if your Reputation with the associated Faction has effectively reset, dropping the difficulty and duration down to their minimums at the start of the Event for all participants. As you successfully complete these missions, you will gain favor with the Faction associated with those Missions, and as a result be served more and more difficult Missions each with substantially better rewards. Among those rewards are Victory Points, which are used to determine your Rank in the Event, as well as what personal Threshold Rewards you will earn along the way.
Some Faction Events will pit multiple different Factions against one another, and you will need to choose which Faction you would like to support. At the end of the event, the winning faction will provide a small bonus to those who supported it.
To participate in an Event, tap the temporary tab on the left side of the screen to view the details, and then tap "Enter Event". Events become accessible at level 8.