Henshin 変身, literally translated as to change or transform the body, is a very common phrase seen in both anime/manga series and tokusatsu series as well. The henshin sequence usually takes place during the climax ending of the show where the protagonists are in trouble and have to activate their magical abilities or transformation devices to help them achieve a more powerful state to defeat their enemies.
In anime/manga series, the most common type of henshin/transformation that you would see would be associated with magical shoujou (e.g. Sailor Moon, Cardcaptor Sakura, Magical Girl Lyrical Nanoha, etc). During their henshin sequence, the girls would usually be in a state of undress but their bodies would be obscured by a magical glow. They will then be given a much kawaii outfit that will magically appear on their bodies.
Here’s a clip featuring the usual Nanoha henshin sequence and the outrageous henshin sequence of Panty & Stocking:
Henshin sequences in tokusatsu series (e.g. Kamen Rider and Super Sentai) are usually much more masculine and cooler because the protagonist are mainly male. They also usually have a catchphrase that they would need to recite, but in the case of Kamen Riders, it is usually just simply shouting out the words “Henshin!”.
Here’s one of my most favorite transformation sequence of Kamen Rider Black RX & Kamen Rider Black:
And here’s a really cool henshin sequence of Samurai Sentai Shinkenger with Engine Sentai Go-Onger.