Website explains alternate-history in advance of upcoming superhero sequel.
X-Men: Days of Future Past is set in two distinct time periods: A dystopian near-future where the (still-living) characters from the first three films battle mutant-hunting robots called Sentinels and the 1970s where the younger characters from First Class are caught up in the early days of "normal" humanity's realization that mutants are among them. The periods are bridged by Wolverine, who time-travels to the 70s in an attempt to prevent the dark future by changing a key moment in history. In advance of the film's release, the new viral site "25 Moments" lays out the alternate timeline of the X-Men world as it currently stands via some clever photoshopping.
The series of 25 images begins with Magneto interfering at the Bay of Pigs in 1962 (from the ending of First Class) and follows through to 2018 with Bishop (Omar Sy) forming a mutant resistance movement. Others alternate between integrating X-Men characters with real events (Magneto is blamed for JFK's assassination, Bolivar Trask accidentally causes the Mad Cow Disease outbreak) showing how this timeline differs from our own (Guantanamo Bay is a mutant prison, The Berlin Wall is still standing) and recapping the events of the previous films.
DOFP's actual storyline is a closely-guarded secret, but it is widely rumored that the film will use the time-travel as a means to "reboot" certain aspects of the series and re-cast certain characters with new actors. A sequel, X-Men: Apocalypse is already in development.
Source: 25 Moments