A torn disc generally refers to a tearing in the annular tissue, the outer layer of the spinal disc. A disc tear is typically caused by a combination of disc degeneration and trauma. When this combination occurs, the central disc material (nucleus) often moves into the torn area of the outer layer of the disc, forming an interpositional disc herniation. A torn disc could also allow for a portion of the nucleus to seep through the tear leading to a herniated disc.
One of the easiest ways to understand a torn disc is to picture a jelly donut. The jelly inside would be the nucleus, while the donut exterior would be the annulus. As the donut starts to get stale and dry up little cracks begin to form, and once these cracks tear, some of the jelly seeps into and eventually through the tear. Although a torn disc is technically a little more complicated than this, this is the basic concept behind it.
A healthy disc is composed of a tough outer shell and a soft inner material called the nucleus pulposus. When a disc tears, the tough outer shell either cracks or tears allowing the inner material to seep through, causing painful disc tear symptoms.
The figures below show the differences between a healthy disc and a torn disc.