INR is the measure of how quickly your blood clots. It naturally varies amongst different people but a normal person will have an INR around about 1.0. If you take anti-coagulation, then your INR will get higher so that if, for example, it is 2.0 then your blood will clot precisely twice as slowly as a normal person.
My INR target is slightly lower than other mechanical valve owners due to my surgeon having confidence in the natural anti-clotting properties of the On-X valve that has been installed. I'm recommended to stay between 2.5 and 3.0. I should never allow it to fall below 2.0.
If INR goes low, say below 2.0, then I run the risk of a blood clot forming somewhere around the valve and shooting up into my brain. This would cause a TIA or even a full stroke - causing partial paralysis and all measure of other horrible things. This is not good AT ALL.
If INR goes high, say over 4.0, then I run the risk of bleeding events. Simplest of these might be seeing blood on the toothbrush, and more complex ones could be bleeding from rectum or if very high, even in the brain. In addition, when high, I'm essentially more vulnerable to injury particularly from Blunt Force Trauma, which can lead to unexpected or exaggerated bruising, or even worse hematomas (like bubbles of blood forming inside a muscle, etc).
In summary, it's MUCH worse to have a low INR than a high one, so if in doubt, aim high.