The katakana are one of the Japanese syllabaries, or set of characters representing single syllables. They were originally used mainly by men in scientific and mathematical contexts, and also in representing the pronunciation of imported Chinese characters.
The katakana are easily recognized because, unlike the hiragana and most kanji, they are angular and blocky, not at all the more graceful, flowing script of the other characters. Today they are used mainly for emphasis (you'll see "baka" written in katakana a lot), sound effects for sudden, percussive sounds (like bangs and claps and such), "gairaigo" or loanwords and foreign words (such as "Bai-bai", "kisu", "haato", foreign names, foreign place names, and almost any Sailormoon attack), slang, and animal words.
The following table displays all of the katakana, sorted by syllable in the customary Japanese ordering.