Mutants came into being several years ago. And society wasn't sure what to make of them. Then President Kennedy was shot. And the bullet curved through the air.
The only explanation would be that a mutant was responsible. So the government looks for ways to remove this threat. And they do by robot warrriors known as sentinels, programmed to identify the mutant gene and destroy the bearer. But as the years passed, the sentinels got smarter. They didn't just seek mutants. They seeked out the humans who could produce mutants, and exterminated them all alike.
And that is why Professor Xaiver and Magneto agree that someone should go back and change history. The prime applicant? Wolverine (Hugh Jackman).
The only problem is that Wolverine wasn't with the X-men at that point in history, and the organization itself was in shambles, with the school closed and only Beast and the professor left in the mansion. And the professor doesn't want any part of his mutant powers any more. It's up to Wolverine and Beast to convince him otherwise, so they and the young Magneto can stop one of their own from setting a disaster rolling.
The future characters' dedication to not just saving themselves but those unlike them is one of the major points of the film, bringing sworn enimes together, risking their lives to the last stand.
Magneto's bit against Xavier is actually rather reasonable, as he accuses him of abandoning his own, and in a way, he did, and the entire storyarc is dependent on his climbing back to self-control and responsibility. One of the other lessons learned is that Xavier could be controlling and over-expectant of others, turning them away.
Wolverine does his best to be the mentor to Xavier that he knew Xavier would one day be for him, even when Xavier refuses to listen.
When he was a child, Xavier took in a child Mystique, telling her that she didn't have to steal any more and was now part of his family, and indeed, he treats all those under him as family.
Ultimately a character risks her life to save a figure who only moments before was urging for her death.
Language is regular, including one F-bomb (referencing an earlier movie), as well as violence (hey, Wolverine is involved, what did you think?). A major disturbance is realizing that in any form, Mystique is naked. In once scene she disguises herself as a fetching French woman, gaining the attention of a Korean ambassador who asks her to take off her clothes for him (and she does as only Mystique can). Quicksilver is a kleptomaniac, and his mother seems just to accept it. There is a hint that Quicksilver is the child of an affair between a human and Magneto. When Wolverine arrives in the past, he's sleeping (naked) with a woman. There is a scene in a nightclub. At one point Wolverine accidentally slashes Shadowcat in the side and she is slowly bleeding out the entire rest of the film. Xavier uses drugs and alchohol to reduce his pain and mutant powers.