Despite the relative uselessness of the widget (but what widget isn't, by nature, useless?), the design of this is unbelievably clever.

Hirgana: the basic Japanese syllabic alphabet. Most commony used.
Katakana: the simplified Japanese syllabic alphabet, most often used to represent foreign words (loan words)
Kanji: the Chinese-derived idiographic alphabet. Used in most advanced writing, as well as names. The most complex of the alphabets, and the hardest to learn.

Hope that helps, and anyone may feel free to elaborate/correct me/mock me horribly.

Kanji is not a phonetic alphabet, like ka ki ku ke ko. But the idiograms represent both meaning and sound (i.e. how to be spoken). To have a good working written vocabulary in proper Japanese, you need to learn about 2000 characters. However, most kanji has furigana (like subtitles), so if you can read hiragana you can get by (and it only has 47 characters).

I thought there was just hiragana and katakana.

Sadly, you need to learn all 3 writing styles. This is because they are usually mixed together in a sentence. But Hiragana is the best place to begin study, as it is the most basic foundation for all writing. But be aware that many written words are part kanji and part hiragana. This is because a kanji only has part of the spelling for a word and needs hiragana to finish it.