Kana (仮名) in Japanese means “syllabary”, therefore a writing system of whose symbols or characters have a purely phonetic nature, and each of them represents a syllable. Kana in Japanese has many variations (such as hentaigana, 変体仮名 – lit. anomalous kana), though only two of them are used today in everyday communication. In calligraphy on the other hand, it is not unusual to write in any of the old styles.
Modern Japanese language consists of two types of kana (hiragana 平仮名, and katakana 片仮名), and kanji (漢字, lit. characters of Han China). The latter is a logographic script, which in opposition to kana, can have complex pictographic semantic and phonetic nature.
Allow me to illustrate it with a simple example. Let us say we want to write down the word “harmony”. In Japanese it is written in kanji as 和(wa), hiragana わ(wa), or katakanaワ(wa). A perfectly natural question is, why anyone would need three writing systems (please note that neither kanji nor kana are alphabets.). The answer lies in both history and linguistics.
Kanji is a writing system imported from China in approximately the 5th century C.E., although single characters started to appear in Japan on imported goods from China as early as the 1st century C.E. However, since Japanese language has completely different grammatical rules to Chinese, a need for a supplementary writing system appeared. The answer to this problem was hiragana, developed out of cursive manyougana (万葉仮名, lit. “kana of ten thousand leaves”), used to write words (suffixes, particles, etc) for which there are no kanji. Cursive manyougana is called sougana (草仮名, lit. draft kana). To simplify it, the evolution of Chinese writing system, it looked as follows: kanji -> manyougana -> sougana -> hiragana.
The cradle of hiragana is considered to be late the 5th century, when its predecessor manyougana came into use. The creation of hiragana is often attributed to possibly the greatest Japanese calligrapher of all times, a Shingon priest (真言宗, Shingon is a major Japanese Buddist school) and Sanskrit scholar Kūkai (空海, 774–835). Kukai, together with Emperor Saga (嵯峨天皇, 786–842) and Tachibana no Hayanari (橘逸勢, 782-842), was one of the famous “three brushes” (三筆, sanpitsu) of the 9th century. Each of them had a profound influence on the development of calligraphy in Japan. They also laid the foundations for wayou shodou (和様書道), a purely Japanese style of sho (書, calligraphy), whose ideas were materialized by Ono no Michikaze (小野道風, 894–966) a century later.