English-style (Roman) letters are called romaji. These are sometimes used for trademarks, advertising slogans, and commands to some old-fashioned computers.
The kanji are Chinese-style characters that the Japanese adopted around the fifth century A.D. Kanji are still used to write many words in Japanese.
The kana are simpler symbols that stand for sounds. There are two kinds of kana: hiragana and katakana.
The hiragana characters are written in a curving, flowing style. They are used for writing some native Japanese words and word endings.
The katakana are more angular characters. They are used mostly for writing foreign-derived words. Words adapted into Japanese from English or other European languages are usually written in katakana.
Many words may be written in either kanji or kana depending on the educational level of the writer and readers. Kana are used most heavily in documents for people who do not know many kanji yet, such as Japanese children. Also, kana are sometimes written above difficult or obscure kanji, to explain the meaning of the kanji.
Usually each kana symbol stands for one syllable. (There are a few kana characters that stand not for syllables, but for modifications to other syllables.)