Equipment Customization is a feature that allows you to make a specific item unique to yourself, while boosting its stats by 20%.
You can tap on the [Customization] button after selecting [Equipment Modification] from the main menu (≡) to view equipment which can be customized (equipment of +10 or higher).
You'll need Butterflies to customize equipment to be unique. Once an equipment is customized, it cannot be sold at the Exchange and it cannot be equipped on other characters, so beware!