What is this dryer part, and how do i fix it?
Your dryer's front drum felt seal's glue failed. The seal keeps gasses from leaking out the front of your dryer into the dryer housing, and also helps support the weight of the front of the rotating drum.

You'll need to get a replacement felt seal and then install it. They're glued in place with heat-resistant glue (apparently your glue wasn't heat-resistant enough). It isn't a hard job if you're handy; you'll have to remove the front of the dryer (probably after propping up the top of the dryer), remove the old seal, and then install the new one.

If you give us the make and model of your dryer we can give you more details.