Before answering your query, I would like to know certain things like the duration from when you noticed the piece of skin hanging under your tongue. Do also state that whether the skin has developed after any particular incident and also the size and color of the same.
It could be an ulceration or something where you might have accidentally bite/tore the tongue underneath on your teeth?
You may want to go to your dentist and get it checked out. If its an ulceration, it should go away on its own in a few days so the fact that its still there is a little odd.
Another possibility could be a canker sore.