What Roosevelt was saying here was that the US economy could get better if people would only have confidence in it.  He was saying that the only reason the Depression was happening was because people were afraid.  So the only thing to be afraid of was their fear--fear was the only problem.

This makes sense if you think about the way economics works.  If people are worried that the economy is going to do badly, they might worry that they will lose their job.  If they worry about that, they won't spend so much money.  If they don't spend money, someone else loses a job because there is not so much demand for products anymore.

We can see this happening some today.  People are worried about the economy and so they don't spend as much as they used to.  This helps make the economy go badly.  So their fear is what is causing the problem.  That is what FDR was talking about.

Franklin Delano Roosevelt made this statement as part of his first inaugural address. He made the statement in an attempt to calm the panic and hopelessness that had gripped the American people because of the Great Depression. The worst days of the depression were actually the period after Roosevelt's election and before he was sworn in, when more banks failed than at any time during the depression. This time is commonly called "the interregnum of despair."

Roosevelt saw that panic and hopelessness were everywhere, and the first step in relief and recovery from the Depression was to calm the American people. To follow through on his comment, his first act as President was to close all U.S. Banks for a "bank holiday." Before they reopened, he conducted his first "fireside chat," in which he asked people to imagine he was sitting in their living room by the fire, having a heart to heart talk. He began his first fireside chat by saying in a calm reassuring voice, "My friends, I want to talk to you about banking." His policy worked. The next day, over 4/5's of the nation's banks re-opened, and there were no more runs.