What is the significance of irreversible ischemia?

Permanent damage. If pictures of the heart during a stress test show a hole in the heart muscle which is there both at rest and during exercise, it indicates that that area has been permanently damaged. No use doing a bypass or angioplasty for that. The damage is done and cannot be reversed.
Heart problem usu. Irreversible ischemia means that an area of your body is not getting blood flow (and can't get blood flow). When it refers to the heart, it likely means that you have had a heart attack in the past and that portion of the heart is no longer getting blood flow. Ask your cardiologist.