What does it mean to have chronic cord compression?

A "squeezed" cord. The spinal cord has less space available then normal due to compression by something (such as a disc herniation, arthritis, tumors, infections, etc.). The word "chronic" implies that this has been going on for a long time and is not a recent problem. Cord compression can be a serious problem with potential paralysis. You should be evaluated by a spinal specialist for this problem.
See below. That there is something, bone, disc material, tumor, something reducing the diameter on the spinal canal and causing pressure/compression of the spinal cord and that the compression is chronic or longstanding in nature.