Can anyone explain the story to me .

Its all about time travel.

Yeah It's not really a true to life story so the writer, director can go a little crazy with the twists, take it as it comes, stop giving yourself headaches trying to figure it out.
Like at the end the mother and Girfriend seem to know each other.

Just like at the beginning of Vanilla Sky it plays Tom Cruise Dreaming about New York Being deserted, but at the start he is dreaming with Sophia's voice on his Alarm clock, he hasn't even met her.
This then turns into Juli's voice when he wakes up properly.
Figure that one out.
HMM Migrane material.

Get the DVD and read the special feature book Philosophy of Time Travel. It explains a lot of the weird stuff that happens in the film.