I wookiepedia'd this and now the New Republic changes it's capital every election year now, so it seems. So the First Order blew up three planets in the Republics capital system, the same system Han went too to drop off Rey, the little soccer ball droid and Finn.
How I've come to understand the new post Endor Star Wars universe is like this:
After Endor, which saw the Super Star Destroyer capital ship of the Imperial fleet destroyed and the loss of several admirals AND an important Grand Moff, along with the death of the Emperor and Vader, there was, naturally, a leadership crisis. Planets rebelled and some joined the rebel alliance, others claimed independence, etc. That's one of the main reasons the imperial fleet lost at Endor and withdrew from the battle without being able to destroy the rebellion, they lost all their leadership.
The empire reorganized and fought the battle of Jakku, which ended with an imperial rout. The rebellion had rallied enough systems to the cause of restoring the republic that they were able to defeat the imperial fleet outright - the imperial fleet also made lots of bad decisions during the battle and suffered a second devastating loss. That was basically the end of the empire. Some small fragments remained but the Rebellion seized Coruscant and reorganized the galaxy. They invited planets to join the republic but did not force them to join.
That's where the New Order was able to sneak in and gain some traction. There were certain planets that chose to remain "imperial" in a sense because they had a democratic right to do so. It seems the Republic recognized this as legitimate. So the "Empire" lived on in some places, but they weren't much of a force. The Republic had/has a massive fleet and millions (billions?) of inhabited planets supporting it.
Luke went on to try and re-start the Jedi Knights as the keepers of peace throughout the galaxy but failed to prevent some key students from turning to the Dark Side. I guess a major risk associated with teaching people about The Force is that people are flawed and might be turned to selfishness and rage for any number of reasons.
Luke taught some kids some lessons, and badda-bing badda-boom, he lost control of certain students. This "supreme leader Snoke" who may or may not have been a student of Luke's started a cult and recruited members, he managed to brainwash Ben Solo who becomes Kylo Ren with stories of his grandfather and promises of power, and any number of other cult-esque strategies that tear people from their families.
This cult gets in contact with whatever remains of the Empire and they form an "Alliance to restore The Empire" kind of thing, and either go on a warpath starting a full on Galactic war, or, they operate as a cult/independent territory and via cold war tactics they terrorize the Republic; it's not clear exactly what was going on politically in "The Force Awakens" (probably by design since Disney knew Abarams only had 1 film on contract and they didn't want him designing the entire new universe).
The First Order seem to have conquered a good portion of the galaxy, or at least intimidated several systems into joining their side, by the time The Force Awakens gets started.
"The Resistance" seems to have been formed within First Order territory, or, as an offshoot of the Republic that would not sit idly by and watch the Empire re-form under the guise of "free-elections" or whatever it is the First Order did to control systems.
So the First Order is either
A) In a full on war against the Republic, but they fear to engage the Republic fleet outright and the Republic Fleet is also unwilling to engage in a decisive battle, so there's a stalemate
B) In a Cold War against the Republic, where they engage in occasional skirmishes that see various territories ceded between one party and the other, followed by peace treaties.
C) Is a cult that is controlling the Republic behind the scenes and can't be crushed because of corruption
Whatever the case may be, they are also fighting a resistance within their territory that is supported by at least some elements of the republic, based on the lines of dialogue we heard in the movie.