The Fitzpatrick scale is a way of classifying skin tone. Unicode uses a Fitzpatrick-based system for emoji skin tone modifiers, which let supported human emoji appear with different skin tones.
Unicode uses five emoji modifiers: light skin tone, medium-light skin tone, medium skin tone, medium-dark skin tone and dark skin tone. These are based on grouped Fitzpatrick types rather than the full medical scale.
In emoji, the modifier is added after a base emoji. For example, 👍 Thumbs up plus a skin tone modifier can display as a single thumbs up emoji with that tone. The same idea applies to many hands, people, professions and activity emoji.
Not every emoji supports skin tone. Faces, objects, animals, symbols and flags usually do not use these modifiers. Skin tone support is mostly for emoji that represent people or body parts.
The Fitzpatrick-based modifiers are one kind of emoji variant. For the broader explanation, see what are skin tone emoji.