Fleets are an organizational structure used by Starfleet Captains to coordinate, socialize, and work toward collective goals. Any Captain worth his salt should strive to be accepted into as large and active a Fleet as possible.
A fleet can be comprised of up to 50 Captains, one of which assumes the rank of Admiral. A number of other Captains can be made Officers of the fleet to assist the Admiral in managing its affairs. A Fleet can be further divided up into Squadrons of up to 5, which can be used to more effectively compete in Events.
Your fleet itself can provide a number of opportunities for personal improvement. Daily Targets allow your entire Fleet to work toward a series of objectives every day that, when completed, provide you and any other active members of your Fleet with valuable resources. Similarly, investing in your Fleet's Starbase can improve your Crew's Skills and your own capacity for productivity.
Fleets become available when your Captain reaches level 7, and can be accessed via the bottom-left button depicting multiple ships. Some Fleets are open, allowing any Captain to join, while others may require a petition or invitation to join. To resign from your current Fleet, simply pull over to the far-right Settings panel and scroll down to leave.