This quote is mostly referring to countries in times of crisis. Fear causes social unrest. People behave irrationally when they are afraid. Countries need to put a cap on that fear in order to avoid chaos. Fear is the enemy, not the people you are afraid of.
I have heard that ninety percent of what one worries about never happens. That means that only ten percent should be worth worrying over. In this case, fear is the problem. Fear can cause one to become paranoid. It can grip one's being and cause one not to be able to function.
This type of worrying is what one has to worry about. Fear is real and can get a hold on any person. That is why there is nothing to fear but fear itself. It is the fear that paralyzes one. The fear can take control over one. Fear can cause heart attacks and other health problems. That is why there is nothing to fear but fear itself. Without the fear, there would be less health problems.
If one could learn not to fear, one could be healthier and happier. If one could learn not to fear, there would be nothing to worry about. Although it is easier said than done, there is nothing to fear. If one fears constantly, life is miserable. That could be what it means when saying there is nothing to fear, so don't.