Fear is a physiological reaction to an external stimulus. It is one of the most ancient and primitive of mankind's emotions, and it is intended to protect us. It did just that for the many hundreds of thousands of years man has been on this planet.
Fear provokes the 'fight or flight' reaction, which is the core of self-defense, if you consider 'self-defense' to be 'self-preservation' and not fighting to avoid looking like a wussy when you could have run away instead.
Fear triggers physical reactions in the body in most people. These reactions include elevated heart rate, increased breathing, sweating, and high adrenalin levels. Many people report tasting copper in their mouths, and shaking afterwards. Mental activity in the brain may change, causing hyper-alertness.
The biggest problem with fear in humans is that there is a third alternative to fight or flight, one which was also hardwired into us as primates, but one which is probably not useful to us nowadays - freezing.
So, when one is suddenly threatened, the brain recognizes the threat and throws up the 'fear' flag, and all this stuff starts happening in our brains, but if we do not either fight or flight, we may freeze; and that's generally a bad thing in a self-defense context.
Martial arts training may help with little fears, like fear of being hit, or fear of harming someone else. But what it does that I feel is more important, is that it trains the pathways of the brain to react in a given way to threats through repetition. In stressful situations, we revert to our training if that training is ingrained deeply enough.
I have seen for myself, even as a martial arts beginner, that people will practice their kata and their self-defense techniques diligently, but when sparring, they'll drop all that and quickly move into a mode more resembling that of brawling school kids; wild swings and out-of-control charges. What happened to all that training? Well, to me, it just means that the training hasn't yet replaced what was imprinted first and deeply on ourselves - the schoolyard reactions to bullies or taunts, for example. I notice that the more highly-trained blackbelts do not lose control and do not revert to brawling. I am convinced that part of the reason that blackbelts win fights is not just because their technique is better (although it is) but because they have been doing it long enough - after years and years, now it has indeed become part of their ingrained response to a threat.
Honestly, I don't worry about fear too much. I don't feel I am too afraid or not afraid enough. I have fear, sometimes. I don't necessarily feel it is something I need to master or control. It is what it is, another emotion. It causes a physical reaction, and I'm aware of that. For the most part, that's a good thing - if I'm afraid, I want my body to be prepping me to defend myself with violence if need be.
More important to me is continuing to train. I am 48 years old and have not been doing martial arts for very long. I have a lifetime of poor responses to overcome and implant new memes, build new pathways in my brain. My responses must become instinctive so that when I need them, they just come, I don't have to think about doing this block or that backfist.
I don't fear fear, and I don't hate fear, and I don't particularly want to master fear. I only want to build new sets of natural responses to what fear alerts me to.