The biggest problem with fear and anxiety is not so much the experience of it, but more what we do to avoid it. Anxiety is often driven and maintained by unobserved/unconscious painful memories of the past and unhelpful predictions of the future. Mindfulness-based therapy can help you to become aware of these modes of thinking/feeling, and focus more objectively on the present.
With mindfulness, you can learn to calm your body and mind so that you observe and accept anxiety. You can learn to see how the untrained mind is agitated by the human condition and how not to allow this general anxiety to fuel your fear in a specific situation. You also gain tolerance for the unpleasantness of uncertainty and also the naturalness of your own imperfection. You have confidence that "life is like this." You cannot and are not supposed to miraculously fix it; rather, you gain the insight that happiness and peace come from relating to life just as it is.
Mindfulness helps you learn to let troubling thoughts pass through your mind without causing you to feel upset. With mindfulness you simply suspend your judgment on whether something is good or bad. This can help you make more realistic assessments of the people and situations that would otherwise make you feel anxious. You can learn to make choices for your life based on your deepest values rather than letting anxiety be in charge.