I think the influence comes because the girls in manga (comics) and anime (cartoons) can take on any role and be anything - a superhero, a badass, or a sweet and innocent school girl.
We've seen their images on clothing here in the US. The trend spiked for a while and then returned to a steady flow. Unlike Japan, where anime girls are used to advertise almost anything.
But more than just the images, a lot of fashion can be drawn from the elaborate battle outfits and cute costumes of the anime girl. Vogue Nippon (Japan) pointed this out in a spread they did at the closing of 2009. They used three of the prevalent manga girl character types to style modern women outside of manga pages.
The schoolgirl has always been what people think of of when they hear the word ANIME - and normally it carries perverted undertones. But the schoolgirl in Vogue Nippon is not sexual; her style is cute and preppy. In Japan, teenage schoolgirls are the main drivers of style and culture.
Anime also features powerful heroines who overcome many obstacles and save the day. Sometimes the heroine looks cute doing it, sometimes she looks strong and dangerous. This heroine wears dark colors to portray some darkness in her life, the one that pushes her to fight, much like the modern woman.
If you want to be the Powerful Heroine, try something black and studded and feel free to show some skin, especially cleavage. Skintight is a must when in comes to fighting bad guys in space or monsters from other worlds.
The romantic heroine is lesser known in the West but has been growing in popularity through Shoujo Manga (basically girly comics that mirror teen dramas). She's a dainty lady, as girly as can be, and normally requires rescuing. She usually gets on my nerves with that.
I do, however, like her style. She has a taste for luxury so feel free to pile on the roses, pearls, ribbons and bows and don't skimp on the lace. Think of a modern Marie-Antoinette with her court if you take this Manga Sweetheart as your inspiration.