A stable joint usually refers to one that does not sublux (partially dislocate) or dislocate fully. The circumstances under which that definition holds true may vary from one expert to another. A truly stable joint stays in the socket for all activities.
Recurrent shoulder dislocations can result in more and more soft tissue damage that eventually contributes to future dislocations. Rehabilitation is often helpful in strengthening the muscles around the joint to help hold it in place.
Restoring natural movement and kinesthetic/proprioceptive awareness is also important. These functions help the shoulder and arm move through space smoothly and with purpose as planned by the brain. Even a small loss in kinesthesia or proprioception can result in a loss of function and recovery during activities that stress or strain the joint.
Any recurrent episodes of the shoulder popping out of the joint (even if you can put it back in) count as an instability. Returning to full activities that require overhead reaching, lifting, and heavy use of the shoulder and arm usually require full strength without fear of reinjury. The physical or occupational therapist helping you with your rehab program will be able to test your shoulder and let you know when you are safe to return-to-work at full capacity.