X-Men: Days of Future Past has a post-credits stinger that really takes a page from the Marvel Studios playbook: it is absolutely incomprehensible to anyone who is unfamiliar with the X-Men comics. We see a huge crowd of desert people on their knees, chanting a name, while enormous Jenga blocks swirl in the air and become the Great Pyramid. The camera swoops around and reveals a skinny, delicate, twinky young boy with grey skin and blue lips who is clearly manipulating the blocks with his mind. Cut to black!
That guy is the mutant villain known as Apocalypse, a mid-80s addition to the X-universe who became kind of inexplicably popular. He was created in the pages of X-Factor, a comic that reunited the original X-Men team (Cyclops, Jean Grey, Angel, Beast and Iceman) as adults; writer Louise Simonson wanted a heavy hitter villain to lead the dopey villain team Alliance of Evil (the original plan was to have Daredevil villain Owl be the leader. What a different X-universe that would be). Apocalypse wasn’t fully formed in his first appearance, and he was just seen in shadows. He was designed by X-Factor artist Jackson Guice and Simonson’s husband, legendary artist Walter Simonson.
Who Apocalypse was wasn’t clear at first; he was intended as a major league threat, and his name certainly gave that impression. He had an agenda: survival of the fittest, culling the weaker members not only of mutantkind but humanity, essentially a big eugenics project. He was introduced in a period of the X comics where mystery was a big deal, and the creators would often bring in new characters for who they didn’t have clear plans (see Mister Sinister, a character who has never made a ton of sense due to his entire history being created via retcon). At first the plan was to make Apocalypse the secret third Summers brother (Scott Summers aka Cyclops and Alexander Summers aka Havok being the other two. They were raised in an orphanage), but eventually a grander history was decided upon.
Apocalypse is the first mutant. He was born 5000 years in Akkaba, a Jordanian city on the Red Sea. With his grey skin and blue lips he always stood out, but with his immense powers (and lots of confusing Marvel nerd history, including the presence of Kang the Conqueror, a time traveler from the 30th century) he became a mysterious figure who reappears throughout history, convincing civilizations to worship him as a god and also manipulating them into wars in order to test their worthiness. He actually helped found SHIELD around 2500 BC when defending Earth against the alien Brood. Seriously.
His real name is En Sabah Nur, which is what those people are chanting in the post-credits stinger. We see him using his super power, which is basically ‘He can do anything.’ Apocalypse is ludicrously overpowered - he’s a genius, he’s super strong, he can teleport, he has pretty much any psychic power he needs, he can control machines, he has total molecular control over the world and, just for shits and giggles, he’s immortal - so the fact that he ever gets beaten is kind of crazy. But he always gets beaten.
Apocalypse has two particularly famous stories. During The Fall of the Mutants Apocalypse offers X-Factor the chance to fight by his side against humanity; when they refuse he unleashes his Four Horseman against them, one of whom turns out to be their former teammate Angel. Thought dead, Angel has been transformed by Apocalypse into the razor-winged Horseman Death, later known as Archangel.
The other famous Apocalypse story is Age of Apocalypse, an alternate universe storyline where a time traveler screws up the past, giving Apocalypse the opportunity to conquer the world, creating a dystopia. The heroes realize they’re living in a bastardized reality and must send one of their own into the past to undo the damage - it’s basically Days of Future Past with a kewler alternate world.
The next X film is scheduled to be X-Men: Apocalypse, which is why you’re seeing this guy show up. What the actual story will be remains to be seen; having an alternate reality story so soon after setting up a new continuity in this time traveling story seems weird. If you asked me to bet money I’d say that Wolverine becomes the Horseman Death, and this is how he gets his adamantium skeleton and claws in the new timeline, since Days of Future Past establishes he never gets captured by Stryker.