Maybe it was the X-men t-shirts and the bag with a bunch of Marvel superheroes on it, but both times I've gone to see X-men: Days of Future Past people have felt I was the guy to pitch a bunch of questions to. And I'm cool with that because comics, in particular X-men comics, are kinda my thing. And sure enough the majority of questions had to do with the film's post-credit sequence which I will get into after this bit of spoiler space...
Okay, so at the end of X-men: Days of Future Past we are taken to a scene in ancient Egypt where a throng of people are chanting "En Sabah Nur!!" to a robed man atop a sand dune using his mutant power to build the Pyramids. The camera rotates around to show his face, revealing he's a teenager with blue lips and greyish skin. This is the immortal Apocalypse, a character born some 5000 years ago in Akkaba, and generally regarded as the first mutant. That distinction went to others for awhile (including Namor) but it has stuck with Apocalypse.
Because of how he was raised, Apocalypse subscribes to the Darwinist theory "survival of the fittest", and has spent his many thousands of years testing himself and others. Due to the involvement of the villain Rama-Tut and acquired Alien technology, Apocalypse has grown in strength and ability over time. He has the power to alter reality and matter, making him capable of literally anything. To maintain his power, he goes into hibernation for lengthy periods of time, leaving his followers in the Clan Akkaba and his personal envoy Ozymandias to handle matters.
That's all well and good, but how is he associated with the X-men? His first appearance comes in the pages of X-factor where he faced the original team of Cyclops, a newly reborn Jean Grey, Iceman, Beast, and Angel. Apocalypse's motives were modest, initially, but then we see that his past, present, and future are uniquely tied to the Summers (Cyclops) bloodline. Apocalypse infected Cyclops' son, Nathan, forcing the child to be sent off into the future when he could be cured. When Nathan returns as the grown-up and militaristic Cable, it's his arrival that awakens Apocalypse once again. Apocalypse becomes obsessed not only with the Summers clan, but with the survival of all mutantkind, in a way making him not too far removed from Magneto ideologically. His aspirations are far greater and self-serving, however.
Apocalypse is the centerpiece of one of the most critical X-men storylines, the Age of Apocalypse. In a story that is very similar to X-men: Days of Future Past, Charles Xavier's son goes back in time to kill Magneto but only succeeds in murdering his own father. With Xavier dead, a new timeline is created in which Apocalypse rules with an iron fist, humans are marginalized or killed outright, and a new team of X-men must be formed to stop him. There have been suggestions that Bryan Singer plans to incorporate elements of this into 2016's X-men: Apocalypse, but all he's seen fit to reveal is a desire to explore the idea of "ancient mutants", which obviously includes Apocalypse.

Kinberg: "The thing that we've spent the most time talking about is not just the visual execution of the character, which is its own challenge. [But] creating a character that's the most powerful I think of any mutant villain that we've seen in the 'X-Men' movies so far. More powerful than Magneto...But we've also been talking about how to give him a real emotional and philosophical underpinning. So he's not just somebody who's out there destroying the world because he can. What he's doing is – in his mind – justified and validated by a real compelling, coherent philosophy. He tries to convert people – maybe some of our most familiar characters – to come to his cause."

X-men: Apocalypse opens May 27th 2016 and will be shot back-to-back with the third Wolverine film.