Alfred Mele breaks down the different things people might mean when they talk about the concept:
According to some people, free will is housed only in non-physical souls; it’s a supernatural power. According to others, whether or not souls exist, free will doesn’t depend on them. People in this second group divide into two subgroups. Some will tell you that the ability to make rational, informed, conscious decisions in the absence of undue force – no one holding a gun to your head – is enough for free will. Others say that something important must be added: If you have free will, then alternative decisions are open to you in a deep way that I will say something about. Sometimes, perhaps, you would have made a different decision if things had been a bit different. For example, if you had been in a slightly better mood, you might have decided to buy two boxes of girl scout cookies instead of just one. But this is not enough for the kind of openness at issue. What is needed is that more than one option was open to you, given everything as it actually was at the time – your mood, all your thoughts and feelings, your brain, your environment, and, indeed, the entire universe and its entire history.
Sam Harris explains why we care:
If the scientific community were to declare free will an illusion, it would precipitate a culture war far more belligerent than the one that has been waged on the subject of evolution. Without free will, sinners and criminals would be nothing more than poorly calibrated clockwork, and any conception of justice that emphasized punishing them (rather than deterring, rehabilitating, or merely containing them) would appear utterly incongruous. And those of us who work hard and follow the rules would not “deserve” our success in any deep sense. It is not an accident that most people find these conclusions abhorrent. The stakes are high.