Accuracy warning: since I'm working with the leaky sieve I call a brain, you are encouraged to verify this information with other sources, and not rely solely on me.
Modern Japanese uses three different writing "scripts" (at least, that's what they're called in Wikipedia): Kanji, Hiragana, & Katakana.
Kanji: These are the symbols that came from China, they are pictographic in origin, and generally one symbol can have a variety of different meanings and sounds. The Chinese symbols do not equate directly to the Japanese ones - over the centuries of use the Japanese have modified both the kanji themselves and often their meaning and sound association. There were several Chinese students in my Japanese class who said it wasn't any easier to actually know Chinese because the meaning shifted (or there were individual strokes that had changed) just enough that it made it a bit confusing. I imagine it's like learning French & Spanish at the same time. Anyway, these symbols were first imported by the court scribes -- the men who'd gone to the Chinese court and who were trying to remake the Japanese royal court as fabulous as the Chinese one was.
Hiragana: Hiragana is a syllabilary where each mark pertains to a consonant-vowel combination (although there are slight exceptions, like for the sound "n"). If I understand correctly, hiragana wasn't imported, but was developed in Japan to express Japanese. It's used when there is no kanji that expresses specific sounds. Also, if the kanji is used to express an obscure sound, hiragana are written (in very small fonts) to the right to explain what the kanji stands for. Technically, all the Japanese language could be written in hiragana, and apparently the younger generations think this is a good idea. Also? Older women's literature was written completely in hiragana because they weren't allowed to learn kanji. The best part about that is a huge portion of the Japanese cannon actually respects women's lit. Even if they do segregate it.
Katakana: the syllabilary for foreign or imported words. It has the same number of characters as the hiragana syllabilary (ie: there's a katakana that relates to every hiragana sound). It's also used on signs and for store names. When a native Japanese word is expressed in katakana it gives it a kind of mystique that can be seen as more modern or kind of cool.
Normal Japanese uses a mix of all of these. And really, although it sounds confusing, it's not that bad. Once you learn hiragana & katakana, it's totally fine. And kanji is a life long learning process, even for Japanese.