Spinal instability can mean different things to different doctors. There isn't complete agreement on one single definition. Some doctors use patients' symptoms as a measure of spinal instability. Painful "catching" during movement, blocked movement, or just persistent pain over time can point to an unstable spine.
Others doctors take X-rays and look for too much slipping or tilting of the vertebrae during movement. If you talk to physical therapists and other exercise specialists, spinal instability is defined in terms of muscle control. Poor posture and weak core trunk and abdominal muscles lead to an unstable spine.
A recent study in Japan used side (sagittal) views of X-rays to measure two things. The measured how much the bones slip or move forward and back while the patient was bending and extending. This is called translation. They also looked at how much the vertebrae angle or tip forward and back during the same motion (angulation).
Then they compared these two measures with patient symptoms. They found that symptoms are worse when there's too much translation. Too much angulation by itself doesn't seem to make a difference. Too much of both movements is linked with chronic low back pain from instability.
Ask your doctor for his or her definition of instability to get a better understanding of your own case.