From my research, inspite of the name, Coconut is considered a vegetable oil.
Further Info:
Cosmetics and skin treatments
Coconut oil is excellent as a skin moisturiser. A study shows that extra virgin coconut oil is as effective and safe as mineral oil when used as a moisturiser, with absence of adverse reactions [5].
Coconut oil can also help in healing Keratosis pilaris by moisturising the affected area. The coconut oil should be applied in the shower, and may cause the KP bumps to disappear.
In India and Sri Lanka, coconut oil is commonly used for styling hair, and cooling or soothing the head (stress relief). People of coastal districts of Karnataka and Kerala bathe in warm water after applying coconut oil all over the body and leaving it as is for an hour. It is suggested by elders that this ritual must be done at least once in a week, to keep body, skin, and hair healthy.
There are also many health benefits to using it in your diet as well.