From what I can tell from the picture they are just to stop the screws from damaging the case when you close it. Put the screw through and then tighten the screw up with the soft part on the case.
Nah, they ground the mobo, you need the contact between case and mobo at screw points
That is exactly what they are for. They are insulating washers. On modern boards, the screw holes themselves are isolated from the rest of the board quite well. On older boards, that was not always the case. Some older boards simply had holes drilled, with no reinforcing built around the holes. If you used a screw with a wide enough head, you could actually touch some of the traces on the board and cause a direct short. That is what those were for. But for all practical purposes, they are not needed for modern boards. The board is grounded via the PSU though, not via the screws that hold it in.