What does it mean if the felt piece that is like a long belt, comes out of your clothes dryer?

That felt liner has come off the dryer, its what helps keep your dryer from chaffing the part of the dryer surrounding the drum, it will need to be replaced.

If you are mechanicly inclined, this shouldn't be all that hard, although you may need to call someone. If the dryer is very old, it would probobly be just as easy to replace it.