The toilet's seat is broken or worn. You've bought a new seat but can't get the old one off.
This is a common problem when an old toilet seat has brass bolts molded into the seat hinge. When you attempt to loosen the corroded fastening nuts, they stick tight, causing the bolt heads to break loose within their molded sockets. No matter what you do, the bolts just spin. The only way to deal with this situation is to saw through the bolts, just under the seat. To keep from marring the toilet's china surface, place a double thickness of duct tape on the bowl, all around the bolts. Remove the blade from a hacksaw, lay it flat against the bottom of the seat, and cut straight through the bolts.
With the old seat removed, position the new one, and insert the bolts through the seat and deck holes. Tighten the nuts. The good news is that you'll only have to do it once. The plastic bolts on new seats will never corrode.