If your going to watch the film, Watch the Anime as well:
So near but so far and beyond our reach or understanding..http://www.isugoi.com/time-traveller-the-girl-who-leapt-through-time-review/
The film and the anime are enjoyable for different reason and even though the concepts are the similar idea but the outcome is very different; now according to the Wikipedia page there is also a Manga and a book by Yasutaka Tsutsui which have been adapted into television series and films. Now the Anime version could be explained but the only thing being is there is slight difference in the names and the event that take place like the differences that Battle Royale has in its media platforms. Indeed the story is about a girl how leaps through time but for example in the Anime the who leaps through time has no idea how she achieves it until the end of the film when things are explained to Her but in the film She drinks a formula that allows Her to time travel. So the Anime can't be compared to the film but both should be watched to get a greater understanding to the over theme of the film, Now the main actress in this film (Riisa Naka) is also the Japanese voice actress for the Anime.
Now Akari Yoshiyama travels into the year 1974 after Her mother is hospitalized because She walk in to a car, which is a very bizarre concept to begin with and then Akari follows Her mothers instructions to go back to the past but Akari doesn't question Her mothers sanity at this point. Akari goes to the past, crashing into Ryota Mizorok who is a science-fiction freak and proves She is from the future by flashing Her mobile and He soon believes Her. Akari then makes it Her mission to track down Her mother from the past and the boy in the photo She has of Her mother. This is not really explained clearly as far as i am aware because it is interfering with past events and on top of that Her mother past self in disturbed by a random stranger asking Her personal questions. Her introduction when a little like " hello, I have a photograph of you and this boy, who is he? You don't know, I will follow you till you tell me who this guy is". Now for the rest of the film Akari follow Her mother around, Her friendship with Ryota changes to something else but the film has a tragic ending and Akari has Her memories erased so She can't remember or going to the past. but never the less the ending is sad and even though She can't remember Ryoka , She still cries when She watches His film that the produced together. Also look out for Mitsuko Delivers(2011), Cafe Isobe (2008), Summer wars (2009) and Love Strikes (2011) which Riisa Naka also stars in.