Roosevelt said this in regards to problems with the economy, but it also applies to life in general. In terms of the economy, when people have fear, they do not spend money, and the cycle of enonomic downturn continues. Therefore, there is nothing that really needs to be feared except for "fear itself." If people would ignore their fear and spend money regardless of how they see the economy, that spending would fuel the economy and there would be nothing to fear. It is a bit of a paradox
It can also apply to life in general. When we fear something, that very fear keeps us from experiencing things and we miss out;the fear wins. It is better to face those fears head on. By doing so, the fear is eliminated and is no longer an issue. Hence, we only have "fear itself" to fear.