The jar was sealed hot. As it cooled, the air trapped inside contracted and left a partial vacuum, and from that moment the atmosphere has been pressing down on the lid with the whole weight of the sky above it. On an ordinary jar that comes to somewhere between ten and thirty kilos of force.
No grip strength beats that, which is why twisting harder keeps failing.
Pry the edge of the lid with the back of a spoon until you hear the pop. That sound is air rushing in. The pressure equalises, and the lid then turns with two fingers.
Hot water works for the same reason from the other direction — metal expands faster than glass, and the warmed air inside pushes back until inside and outside roughly agree.
All along the opponent was a pressure difference, and a pressure difference can be cancelled instead of overpowered.