Spoilers for Star Wars: The Force Awakens within.
When the original Star Wars came out you didn't need much political context - there was an Empire and there was a Rebel Alliance fighting against it. We knew the Empire was new-ish, because the Senate was disbanded during the course of the movie, but that was all you really needed to know. The bad guys looked like space Nazis and we were off to the races.
It turns out we might need slightly more political context for Star Wars: The Force Awakens - context the movie doesn't supply. But it turns out some of the now-canon tie-in books do, and I've spent a little while at Wookieepedia figuring out just what the hell is up with The Resistance and the First Order.
Why do we need some context? Because the last time we saw the Star Wars galaxy the Empire had fallen - see the celebrations in the streets of Coruscant in the Special Edition - but now we're right back in what looks exactly, completely like the political context of the first Star Wars movie. There's an evil Nazi-like Empire running around and there are good guy Rebels in a hidden base. Not only is like nothing changed since Jedi, it's like we went back in time to the first film. But it's not quite so simple.
A little history: the Galactic Civil War didn't exactly end with the Battle of Endor. While that was the decisive turning point, it seems to have gone on for one more year, with the final final battle happening at Jakku. The Rebels formed the New Republic while the shattered remains of the Empire limped out to the Outer Rim, where you can easily disappear. It's wild space out there. Think of it like the Nazis who escaped to Argentina.
The Rebels set up the New Republic and, for reasons that escape me, established their capitol in the Hosnian System, on Hosnian Prime. While I get that Palpatine probably stunk up Coruscant, that planet was the seat of power of the Old Republic as well - I don't quite know why they moved. Maybe it's so that when Starkiller Base blows up a planet it isn't Coruscant, even though the planet blown up in The Force Awakens looks, for all intents and purposes, like Coruscant.
While the New Republic was getting back into the business of being a democratic society - ie, a lot of bickering and fighting and stalemates and poltical nonsense - the shards of the Empire were reforming on the Outer Rim under the guidance of the mysterious Supreme Leader Snoke. Most in the New Republic ignore the growing menace of the First Order, but not Leia - after all, the Organas have a history of seeing bad shit coming down the pike. She pleads with the New Republic to deal with the FIrst Order, but everybody thinks she's overreacting; finally she's able to convince the powers-that-be to let her go off and lead a small resistance group which she then imaginatively names The Resistance. Basically this is like when the US sends advisors and some money and weapons to support an insurgent group in a communist (or now Islamic) country. The New Republic isn't fighting the war - the logo of The Resistance is pointedly the same as the logo of the Rebel Alliance, not The New Republic (which, to be fair, is pretty similar anyway) - but they're kind of fighting a proxy war led by Leia.
That's the basic set up; when The First Order blows up Hosnian Prime it's basically like a terrorist group going after the US because it has supported fighters in their home region. It's an extravagant move, of course, but The First Order, influenced greatly by the Empire, seems to think big.
When it's all laid out it's simple, but the movie really obfuscates it, leaving many people to scratch their head in confusion about the exact state of the galaxy at the opening of The Force Awakens. The true mystery - one that doesn't feel like a storytelling fumble - is just who and what Supreme Leader Snoke is. It seems clear that his recruitment of Ben Solo/Kylo Ren was a turning point in the struggle for The Resistance - this must be why they need Luke Skywalker so badly. But what role Snoke played in the formation of the First Order and how he turned Ben Solo are stories that remain to be told. The rest of this stuff was simply inconveniently hidden in books (many of them young reader novels, no less!).