The bearhug is a wrestling hold, not seen in pro matches much these days because most younger wrestling fans find it boring. It is considered a “power” hold because it takes considerable strength and effort on the part of the applier to put on and keep on. It can be used either as a direct pain or “submission” hold, or (my preferred way) as a “weardown” hold, where it saps the energy of the victim, making them weak and can even render them unconscious.
“Ragdoll” refers to the state of just being all limp and unable to move or even support your own weight. You’re conscious, but you have no strength to do anything, you can’t stand, you can’t hold yourself upright, you’d literally be just hanging as a dead weight in the guy’s arms.