The oil-soluble extract coming from the edible, orange part of the carrot. It is created by macerating the carrot root in a carrier oil such as sunflower or olive oil, and the resulting thing (base oil + carrot root extract) is often called carrot oil or carrot root oil. (Not to be confused with carrot seed oil, that can be fixed or essential and comes from the seeds.)
The root extract is known for containing the orange pigment beta-carotene, aka provitamin A. It is a famous molecule for being a potent antioxidant, suntan accelerator and having skin-regenerative abilities. Carrot oil also contains vitamin E and some fatty acids that give the oil further antioxidant and barrier repairing properties.