To be unnerved is to lose courage or become uneasy. You might think you want to try bungee jumping, only to feel unnerved once you're standing on the edge of a bridge preparing to jump.
The word nerve can mean "strength, steadiness, and courage," as in "I planned to confront him, but then I lost my nerve." It makes sense, then, that being unnerved means a loss of that same steadfastness or bravery. So you might be unnerved on airplanes or when confronted with spiders, depending on what makes you feel a little less than brave.