freedom of self determination and action independent of external causes
Can the definition be any more condemning? Action independent of external causes?! This means that free will is incompatible with the principle of causality. In the physics community, we quickly toss away theories that are non-causal. If events do not have a cause, then you cannot predict them. They are, in effect, supernatural events. In fact, it hard to think of a scenario where one could argue for having free will without believing in some sort of supernatural "spirit" or "soul" that isn't affected by natural events.
Now someone might say "quantum mechanics has shown us that we cannot always predict what will happen with absolute certainty, perhaps this leaves room for free will?". This is a good try, but it still doesn't cut it. It's true that in modern physics things cannot be predicted with absolute accuracy, but we can predict probabilities of events occuring. So in principle, I could compile all events that happened in your lifetime into a huge computer, complete with all genetic information that may be relevant, and if I knew what events you would later observe I could predict the probabilities of you doing certain actions and of your brain generating certain thoughts. Sure, it would take a huge amount of computing power and a great deal of initial data to compute these probabilities, but they could be computed in principle, and that is all that is necessary to invalidate the idea of free will.
The ambitious atheist might try to conclude that that absence of free will completely destroys the idea of ChristianTM morality because if humans don't have free will, then they cannot choose their life and it makes no sense to punish nor reward them for their actions as Christian dogma describes. But I have to say, for the sake of intellectual honesty, that I don't believe my argument applies to Christianity in this way, or any other religion for that matter. The reason for this is that Christians, for example, presuppose the existence of a supernatural realm, and who is to say that the principle of causality applies in that realm? Christians actually believe in souls, spirits, angels, and demons. So it's quite easy to see how a Christian might be able to argue that the supernatural realm is non-causal. However, if they do so, some of their ideas of God, particularly those which are related to his anthropomorphic character, are bound to fall apart. For example, if God lives in the supernatural realm, and is a non-causal being, then why should one pray to him? Your prayers don't necessarily cause him to think about your situation, because his processes are not caused by external events! Any story from the Bible where God reacts to earthly events also becomes suspect, since the supernatural world is not causal. The Christian may then argue that some aspects of the supernatural are causal, while others are not. And it's obvious that the things which are causal and those which are non-causal will depend on what it needs to be to be consistent with his worldview. I guess that's the convenience with believing in a magical world where anything goes and one can simply wish it to be true and it is....
Outside of religious debates, what significance does the absence of free will mean to the normal person? For one, it's something that must be kept in mind when one considers the concept of justice. If people do not actually make choices in a free manner, it makes no sense to punish them for their "wickedness". Instead, one must look for the causes of bad behavior and think about logical ways to prevent it from happening in the future.
I personally am not concerned with my lack of free will. My choices and thoughts are determined by the experiences I've had in my life, and that's all that I need, not to mention the only thing that makes sense to me.