When the first teaser for The Force Awakens was released back in November it had Storm Troopers, TIE fighters and a bad guy in black with a red lightsaber, it is so very familiar and yet different. Was the Empire still around? What happened to them after Return of the Jedi? Then we were told these new Storm Troopers we members of The First Order, so who exactly are the First Order?
“That all came out of conversations about what would have happened if the Nazis all went to Argentina but then started working together again? What could be born of that? Could The First Order exist as a group that actually admired The Empire? Could the work of The Empire be seen as unfulfilled? And could Vader be a martyr? Could there be a need to see through what didn’t get done?”
―J.J. Abrams
We got this new quote from Empire Magazine on Tuesday, which confirmed what many suspected, the First Order is built from the remnants of the Empire. I like that JJ and Kasden used history to shape their vision of what would happen after Endor. Many Nazis did go to Argentina after the fall of the Third Reich and there may have even been a plan to regroup, it just never happened. I see the Star Wars galactic situation like this, after the defeat of the Empire at Endor and the subsequent battles the Empire was sent to the running, scattered to the far parts of the galaxy. But they regrouped and reorganized under unified leadership of Supreme Leader Snoke. They built themselves back up, training new recruits, gaining assets and building new updated star ships. This new organization puts value on ability over any other factor (Race, sex, etc), they have a goal and need the very best to accomplish it. The goal is to reestablish the Galactic Empire under a new Emperor, the current Supreme Leader Snoke (A title not far from Supreme Chancellor). This official merchandise towel implies the goal is to rule as the Empire did before also.
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The question then is why called themselves the First Order instead of continuing to call themselves the Empire. I have two ideas as to why.
The first is related to Order 66 from the Revenge of the Sith. According to Legends materials there were 150 contingency orders for the grand army of the Republic however we only know of 5. After the formation of the Empire they would most likely have changed but not necessarily been done away with. Could the first of these be “Maintain the Empire at all costs”? If so then this group has named themselves for their goal. They are the loyal ones, those that follow the first order and will restore the Empire and bring peace to the Galaxy.
The other idea is based on the Knights of Ren and who Snoke is. The First Order is under the control of Snoke and Kylo Ren is one of the First Order leaders.This puts known dark side users at its head. If the Knights of Ren are an old order, and order older than Jedi, older than the Sith, and view themselves as the first order of Force users they would name their military after themselves in a way. Only those that can use the Force can be in the Knights of Ren but everyone else can join the army of the First Order. Their goal is not only to create a new Empire but to be the only order of Force users, hence why they attacked Luke’s academy and are tracking down Force users and artifacts. 
To me both one of these would be awesome and it could be a mix of the two. In fact the leaks we have about the new novel Aftermath tell us the Emperor was exploring beyond the outer rim and setting something up out there. This combined with the introduction of the acolytes of the Beyond(Where Snoke and/or the Knights of Ren come from?) implies a little of both. What we do know is the First Order is a threat to the Galaxy at large and those that value the beliefs of all those who died in the war against the Empire. The dark side is guiding them and the only hope for the Resistance is the awakening of the light side of the Force.