A "Sequestrii" is a normal occurrance and, as your dentist explained to you, should be left alone. It has two decisions to make: either it will heal and reattach itself or it won't. And we want this to heal! So you must take particular care of it, extending the directions that you were given directly after your extraction. No smoking, keeping it very clean; that kind of thing.
This bone is not tooth. So there's a 50/50 chance that it is still attached to your other bone. That is why it should not be messed with, as you could either greatly stall it's healing process or destroy it all-together.
If the bone does die, your body will obviously reject the necrotic tissue. This may be a somewhat uncomfortable, painful process. It may come out on it's own and it may fester. That is when a dentist/oral surgeon would re-enter the socket and remove the tissue.
The best possible thing you can do for yourself is just to leave it be and keep caring for it very closely, hopefully aiding to a successful and speedy recovery!
Best of dental health to you!