Botanical, Synthetic, Animal
Fragrance is the very unspecific word used to describe the mixture of dozens, or sometimes even hundreds, of the various fragrant compounds that give a skincare product its characteristic scent.
Fragrances can be of botanical origin (e.g., various essential oils and their isolated compounds like limonene or linalool), animal origin (e.g., musk, castoreum, civet, or ambergris), or synthetic (various fragrant compounds can be synthesized from simple chemical ingredients).
The concern with fragrance in skincare lies in the fact that they often cause a contact skin allergy for more sensitive individuals. The allergen potential lies in the chemical structure of the fragrant compound and not in whether or not it is natural. Many natural fragrances, such as limonene, are highly allergenic.
If the manufacturer does not disclose what went into the fragrance, then you have no way of knowing its exact composition. Fragrances and perfumes are often trade secrets.