Formal skills generally means skills that have been taught and learned and then practiced. The implication is that someone with some expertise taught you to do something. You learned how to do it and you have actually done it. For example, drawing a blood sample from a patient is a formal skill that you aquire by someone with some expertise teaching you how to do it and you watch and learn how to do it and then you have practiced drawning blood from a patient. Formal cooking skills generally means learning to cook by going to classes with an instructor. Compared to learning to cook at home from a book.