Hentaigana (literally, "variant kana"), are alternative kana forms for Japanese syllables which were used at various times and places in Japanese history but which are now no longer in common use. Like the modern hiragana and katakana syllabaries, the hentaigana evolved as simplified forms of the "manyogana" kanji characters originally used to represent the Japanese language in the 8th century.
Some of these characters had several simplified forms, two of which became the modern hiragana and katakana forms for a certain syllable, and the others of which are now considered hentaigana. In other cases, the hentaigana evolved as simplified forms of completely different characters, as manyogana generally had several different kanji which could be used to represent each Japanese syllable.
Hentaigana were used interchangeably with the modern kana in accordance with regional, cultural, and personal preferences from the 8th century until 1900, when a national orthographic reform mandated that only a single kana in each of hiragana and katakana be used nationwide to represent each syllable.
Hentaigana are still used today in a few specialized circumstances, most famously in the word "kisoba" on the signs of soba shops, and sometimes on traditional documents used issued in martial arts and religious schools. However, given that the vast majority of Japanese people have no idea how to read hentaigana, their practical utility is limited.
Note that the two-character compound "hentai" in "hentaigana" has a different second character from the Japanese word for "perversion", which is also prounounced "hentai". However, the two words share the same etymological root conveying a sense of "abnormality".