According to the magazine, the reason for time travel has been revealed. Wolverine is going back in time in order to stop Mystique from doing something that changes things forever.
The magazine writes:
"[Wolverine's] mission: to find Charles Xavier (James McAvoy) and Erik Lehnsherr (Michael Fassbender), and recruit them to help him stop Mystique (Jennifer Lawrence) from doing something really stupid."
There is also a bit of dialogue that director Bryan Singer revealed to the magazine as well!
"There’s a line that Fassbender says that may make it," reveals Singer. "He says to Wolverine, ‘You spend the next 50 years trying to bring me down?’ Wolverine says, ‘Pretty much.’ Magneto says, ‘How did that go for you...?'"
Finally, you've seen the trailer (if not check it out below or see it again!) and should know that Logan has some grey hairs in the future timeline of the film.
"There’s the Logan we find in the post-apocalyptic ruins of 2023, grim, grey-streaked, struggling to stay alive—along with his fellow X-Men—in the face of an onslaught from giant mutant-hunting robots, the Sentinels. "
So what does Mystique do? Whatever it is is seems like this is why she's being dragged toward Magneto in the trailer.
X-Men Days of Future Past is out in theaters on May 23, 2014. (And please show us some Sentinels in action already!)