In a nutshell: Magneto’s Brotherhood assassinates Senator Robert Kelly and increases anti-mutant fervor worldwide. In the U.S. the Sentinel program is created to capture all mutants. The machines realize that all humans have the potential for creating more mutants and proceed to eradicate all human life. Someone from that future, Kitty Pryde in the comic, Professor X in the second animated adaptation, send messages through time to prevent said future from happening.
The movie will be a very loose adaptation of the comic book story, as Kitty Pryde is not yet born in the movie universe, Senator Kelly has been used, and Wolverine is not in the First Class storyline. According to some speculation, this movie would serve as a bridge between First Class and original movies. But as long as they capture the essence of the story, it will be fine.
The plot of the next movie is all speculation right now. Fox remains tight lipped about this project. It does not want to tip its hand with too many details just yet. What is known is that the title Days of Future Past has been registered with the MPAA Title Registration Bureau. So that means the movie will be distributed under that title. It’s expected to come out in 2014.