Bananas are good sources of potassium and therefore a good pick me up food after illness, an operation or particularly the runs in piggies. I only feed the banana flesh when they have been ill - because the banana fruit is very high in sugars. So it gives them energy and minerals, and is easy to mash if you need to spoon or syringe feed.
I wouldn't feed a lot at a time, but a banana skin once or twice a week between my four when they are well is fine. I do sometimes give a bit of skin and leave the rest in the fridge, it keeps well enough like that. They can easily digest the skin, they have a better digestion for vegetables than we have. They may not like it to begin with, as with humans any taste is learnt, so don't worry if they ignore it to start with, just keep trying as it really is a good pick me up. (Also you get to eat a banana yourself which is good for you!)
Please note this is just how I do things, don't take it as gospel, but please do be aware that if you regularly feed the flesh of the banana then you are encouraging the kidneys to work too hard because of the sugar levels.