Henshin (変身, henshin) is the Japanese word for "transformation". In the Kamen Rider Series, it is a common catchphrase for when the Rider transforms, as it might have been a word Shotaro Ishinomori himself had invented.
With the exception of the wordless transformations of the Oni Kamen Riders in Kamen Rider Hibiki, the "A - ma - zon!" cry of Kamen Rider Amazon, and the "Set up!" call of Kamen Rider X, while Shin just using anger, every Japanese Kamen Rider uses the phrase when assuming Rider Form.
Some Riders have similar catchphrases for when they assume different forms while still in rider form such as Kamen Rider Kuuga's Cho Henshin (超変身, Chō Henshin, Super Transformation) phrase.