Well, those ribbons you are talking about are not exactly ribbons but feelers appearing to be like ribbons.
A Feeler is an animal organ such as an antenna or palp that is used for testing things by touch or for searching for food. And as for what's their use, it sends a soothing aura from these feelers to calm fights and also uses it to affectionately embrace its trainer like holding the trainers' hands with these. And as shown in the anime, Sylveon can also use these to attack opponents for example when Serena's Sylveon uses Fairy Wind.
Hope I helped! :)))
