Its basically an organizational and ease of use thing.
The Fleet Organization Window does not allow you to select multiple ships at once to move them into different fleets, you have to move them individually between formations. With sub-fleets you can group a number of ships together into their own fleet then order that fleet to join another fleet as a Sub-Fleet. That sub-fleet is considered as part of the parent fleet and will no longer show up on the system map or be listed on the galaxy map when you try to select a ship from the dropdown list. It is still visible on the Fleet Organization Window. You can detach and form a new fleet or drag-and-drop to a separate fleet at a later date just like a single ship.
Squadrons are a similar concept to a sub-fleet but assigned to a specific carrier ship.
A Strike Group is the entire complement of squadrons on a carrier. Aurora automatically forms a Strike Group when you hit 'Launch All' button with a carrier (or fleet/sub-fleet with a carrier) selected. This Strike Group is its own fleet with each squadron creating a sub-fleet, however it is still 'attached' to the carrier they are launched from and the damage/kill statistics of the Strike Group is recorded to the home carrier's own statistics as well.
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In my current game (still in 2. 02 but still relevant) I form my ships into 4-ship divisions (fleets) as my smallest tactical unit. If I have a situation where I need a ship to defend something or chase down an enemy then I send out a division. I generally try to form these divisions from the same type of ship (corvette, frigate, cruiser, ect. ) if not the same class.
For example, I use frigates as lightly armored, long duration, patrol and picket ships while my destroyers have a similar tonnage but are more heavily armored and used as light combat and escort ships. By keeping them in separate formations, I can easily send out ships to do missions they are more suited for.
My next sized unit is the squadron. This is both an administrative and tactical formation (I have an Admin Command that I assign individual divisions (fleets) to and those divisions (fleets) may join together to form a larger fleet under the same Admin Command). I use these formations for when I'm moving a lot of ships to a different area, for large scale offensive or defensive operations, or to declutter the fleet lists in orbit. I have the divisions join the squadron as part of sub-fleets to enable them split off in an organized manor once they are in their new area. Squadrons can mix different division types together to be able to perform a wider variety of tasks.
Two examples are my carrier and patrol squadrons. My carrier squadrons have a division of 4 carriers for long range strikes, a division of cruisers for heavy escort, a missile defense division of 2-4 ships, and one or two divisions of destroyers for light escort. My patrol squadrons have a division of patrol cruisers (defensive ships designed for long duration missions), a division of missile frigates for long range firepower, a division of beam frigates, and a division of patrol ships (similar concept to the frigate, but smaller).
Each division is its own separate sub-fleet in the fleet, allowing me to spit off a division for independent action if needed with ease.
I currently have two types of carriers in service, light carriers and carriers. My light carriers have two squadrons based on them, one squadron of 24 250-ton beam fighters (armed with either gauss cannon or single shot 10cm rail guns) and a squadron of 24 250-ton fighter/bombers (armed with 7 Size-1 or 3 Size-2 box launchers). My carriers carry the above squadrons plus a squadron of 12 250-ton bombers (6 Size-2 box launchers), a squadron of 12 250-ton torpedo bombers (2 Size-6 box launchers), a squadron of tankers (either 8 500-ton or 4 1,000 ton small craft), and a squadron of recon craft of either 8 250-ton fighter-scouts (2 Size-2 box launchers and R100 active and passive sensors instead of just the R1 active sensors on the other fighter craft) or 4 500-ton early warning craft (25-ton R-1 and R15/R100 active and 25-ton EW and thermal sensors).
My light carrier's strike group has two sub-fleets that are the two squadrons and my larger carrier's strike group has six sub-fleets for its six squadrons. I can launch the strike group, split off the various squadrons to perform separate tasks and then have them either rejoin or return home at my discretion with just a few clicks instead of having to drag 24-64 individual fighters into separate groups manually.
