The melacha of mafshit can apply to any animal – mammal, fish or bird – that has a skin which can be removed.
Mafshit is one of those melachos that one is not likely to encounter very frequently. For a variety of reasons, the melacha does not apply to cooked animals that are being eaten as food, so removing the skin of chicken or fish on one’s plate would not constitute mafshit (although one must still be careful of boreir).
Skinning a raw chicken would be mafshit. Since raw chicken is muktzeh on Shabbos, this is still not likely to be an issue on Shabbos, though it might be on Yom Tov, when cooking is permitted.
This is just an introduction to the concepts of the melacha of mafshit; it is not a substitute for a full study of the halachos.