Oh, well...yeah, apparently a Sylveon's ribbons are actually part of their body. I'm not really sure how that works, either, but Twizzle seems to enjoy having them. She likes using them to pick things up or hold onto my arm. I think the Pokedex said that a Sylveon can use them to read people's feelings, too.

[Twizzle makes a heart shape with her ribbon-like feelers and winks. She finds her flesh ribbons very useful, for a number of reasons.]