[Mild SPOILERS ahead for Star Wars: The Force Awakens.]
Star Wars: Episode VII - The Force Awakens picks up more than thirty years after the events of Episode VI: Return of the Jedi - and though many things have changed in the Star Wars universe since then, other things have not. The Galactic Empire is gone, but its remnants have regrouped to form The First Order; the Rebel Alliance has become The Resistance, lead by one General Leia Organa/Skywalker (Carrie Fisher); and the First Order's totalitarian forces seek to maintain an iron grip on the galaxy by way of a powerful super-weapon.
The similarities between that new super-weapon, the Starkiller Base - which can be seen on the official Force Awakens poster (see it above) - and the Death Stars from Star Wars movies past have not gone unnoticed by fans. However, Force Awakens' co-writer/director J.J. Abrams has offered his assurances that the influence of the Death Stars on the First Order's powerful base is, in fact, acknowledged in the film... and is a key element of its narrative, in many ways.
Here is what Abrams told EW, with regard to the Starkiller Base in Star Wars: The Force Awakens:
“It is very much — and it’s acknowledged as such in the movie — apparently another Death Star. But what it’s capable of, how it works, and what the threat is, is far greater than what the Death Star could have done. Starkiller Base is another step forward, technologically speaking, in terms of power.”
Indeed, it's already been revealed that the Starkiller Base is far more powerful than either Death Star and is, in fact, "capable of destroying entire star systems." The weapon appears to have been inspired by the Sun Crusher: a weapon that, in the no longer canon Star Wars Expanded Universe mythos (now known as Star Wars Legends), could destroy entire solar systems. Non-human scientist Qwi Xux was responsible for designing both the Death Star and Sun Crusher in the Star Wars EU, though in Episode II: Attack of the Clones it was established that Genosian scientists were partly responsible for crafting the Death Star plans, as far as the official Star Wars canon goes. It remains to be seen who will be the engineer behind the Starkiller Base in The Force Awakens - or if that matter will even be addressed in the movie (seeing as it probably won't be all that relevant, plot-wise).
The key thing to know about the Starkiller Base is that it serves as a reflection of The First Order's general philosophy in The Force Awakens, according to Abrams; that is, to succeed where the Galactic Empire failed, the First Order seeks to be even more powerful and threatening. Domhnall Gleeson (Ex Machina), who plays First Order military leader General Hux in the film, elaborated on that idea during his own interview with EW, describing his character's outlook (and those of several of The First Order's members) as follows:
“There’s an air of superiority, and being better than those people around you. He’s pretty ruthless. A strong disciplinarian would be a mild way of putting it. You don’t get that high up in your life that quickly unless you’re pretty ruthless. You have to put a few people down on the way to get there.”
Hux, like many a member of the Galactic Empire before him, foremost wants "to lump everything in its place and just have power," as Gleeson put it. However, whereas military figures in the Galactic Empire were all exceptionally subservient and loyal to Darth Vader (lest he Force-choke them to death for his failures), Gleeson indicates that in Force Awakens there may be some tension (and, in turn, a struggle for power and control) between Hux and the First Order's own Force-wielding agents: Kylo Ren (Adam Driver) and the Knights of Ren. As Gleeson put it, with regard to Hux:
“He’s kind of opposite Kylo Ren. They have their own relationship, which is individual and unusual. One of them is strong in different ways than the other. They’re both vying for power.”
While it sounds as though certain rumors about Gleeson's Force Awakens character are off - for example, that he's secretly a double-agent seeking to destroy super-weapons like the Starkiller Base - other rumors might be more accurate, such as the claim that the Resistance and First Order have been locked in a galactic Cold War for some time, leading up to events in the film. Hux looks to use the First Order's military forces and super-weaponry to serve his own ambitions (read: gain even more power), so the question remains: is Kylo Ren and/or possibly his master, Supreme Leader Snoke (Andy Serkis), after something else?
Kylo's apparent obsession with fulfilling his "destiny" and finishing the work of Darth Vader indicates that he does, in fact, have more specific interests than just accumulating even more power - as Gleeson suggests. It's a fair bet that the as-yet unknown status of Jedi Master Luke Skywalker (Mark Hamill) and the role he plays in The Force Awakens has something to do with all this too; hence Luke not being included in the marketing campaign for the film (to better preserve secrecy).
Star Wars: The Force Awakens hits theaters on December 18th, 2015, followed by Rogue One: A Star Wars Story on December 16th, 2016, Star Wars: Episode VIII on May 26th, 2017, and the Han Solo Star Wars Anthology film on May 25th, 2018. Star Wars: Episode IX is expected to reach theaters in 2019, followed by the third Star Wars Anthology film in 2020.